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#1076 2020-02-29 23:14:53

ganesh
Administrator
Registered: 2005-06-28
Posts: 30,869

Re: Series and Progressions

Hi,

SP#605. A sum of $700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is $20 less than its preceding prize, find the value of each of the prizes.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#1077 2020-04-01 01:29:08

ganesh
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Registered: 2005-06-28
Posts: 30,869

Re: Series and Progressions

Hi,

SP#606. Show that

form an Arithmetic Progression where
is defined as
. Also, find the sum of the first 15 terms.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#1078 2020-04-22 16:05:46

666 bro
Member
From: Flatland
Registered: 2019-04-26
Posts: 335

Re: Series and Progressions

a1, a2, a3 forms an A.P with d=4.
They are:
a1=7
a2= 11
a3=15
S15= 525.


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#1079 2020-04-22 20:43:07

ganesh
Administrator
Registered: 2005-06-28
Posts: 30,869

Re: Series and Progressions

Hi 666 bro,

Neat work!

SP # 607. Show that

form an Arithmetic Progression where
is defined as
Also, find the sum of the first 15 terms.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#1080 2020-05-01 00:02:56

ganesh
Administrator
Registered: 2005-06-28
Posts: 30,869

Re: Series and Progressions

Hi,

SP # 608. The sum of 15 terms of an Arithmetic Progression with common difference 6 is 780. Write the algebraic expression of the sequence.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#1081 2020-05-31 23:38:26

ganesh
Administrator
Registered: 2005-06-28
Posts: 30,869

Re: Series and Progressions

Hi,

SP # 609. Write the algebraic expression for the sum of the sequence.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#1082 2020-06-25 22:29:10

666 bro
Member
From: Flatland
Registered: 2019-04-26
Posts: 335

Re: Series and Progressions

Sp#609: 2sₙ -n(2a+(n-1)d) =0


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#1083 2020-06-25 23:55:18

ganesh
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Registered: 2005-06-28
Posts: 30,869

Re: Series and Progressions

SP # 610. Write arithmetic sequences with 100 as the sum of the first four terms.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#1084 2020-06-27 02:36:41

666 bro
Member
From: Flatland
Registered: 2019-04-26
Posts: 335

Re: Series and Progressions

Sp#610 the sequences are:
(1) : 10, 20, 30 , 40 where
a = 10 & d = 10.
(2) :25, 25, 25,25 where
a = 25 & d = 0.


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#1085 2020-06-27 12:57:35

ganesh
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Registered: 2005-06-28
Posts: 30,869

Re: Series and Progressions

Partially correct. Good attempt!

SP# 611. Consider an arithmetic sequence

.
(a) Find the algebraic expression of the sequence.
(b) Is there any counting number in the sequence?


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#1086 2020-06-27 19:19:30

666 bro
Member
From: Flatland
Registered: 2019-04-26
Posts: 335

Re: Series and Progressions

SP#611 (a) : sₙ = ( n^2) + (10/7)n.
   (b) :   no,

Last edited by 666 bro (2020-06-27 20:34:46)


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#1087 2020-06-27 23:42:51

ganesh
Administrator
Registered: 2005-06-28
Posts: 30,869

Re: Series and Progressions

SP # 612. (a) What is the sum of first 20 natural numbers?
(b) The algebraic form of an arithmetic sequence is 6n + 5. Find the sum of the first 20 terms of this sequence.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#1088 2020-06-28 23:06:13

666 bro
Member
From: Flatland
Registered: 2019-04-26
Posts: 335

Re: Series and Progressions

(a) : s₂₀ = 210.

(b) : s₂₀ = 1360.


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#1089 2020-06-30 14:17:32

ganesh
Administrator
Registered: 2005-06-28
Posts: 30,869

Re: Series and Progressions

Well done!

SP # 613. Sum of first n terms of an arithmetic sequence is 3n² + n. Find the first term and common difference of this sequence.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#1090 2020-06-30 23:03:12

666 bro
Member
From: Flatland
Registered: 2019-04-26
Posts: 335

Re: Series and Progressions

Sp#613: a= 4 & d=6.


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#1091 2020-07-01 03:08:47

ganesh
Administrator
Registered: 2005-06-28
Posts: 30,869

Re: Series and Progressions

Good work!

SP # 614. (a) The fifth term of an arithmetic sequence is 40 and 10th term is 20. What is the 15th term?
(b) How many terms of this sequence make the sum zero?


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#1092 2020-07-12 21:28:40

ganesh
Administrator
Registered: 2005-06-28
Posts: 30,869

Re: Series and Progressions

Hi,

SP # 615. The sum of first ten terms of an arithmetic sequence is 350 and the sum of first five terms is 100. Write the algebraic expression for the sequence.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#1093 2020-07-31 23:49:00

ganesh
Administrator
Registered: 2005-06-28
Posts: 30,869

Re: Series and Progressions

Hi,

SP # 616. What is the difference between the sum of the first 20 terms and the next 20 terms of the Arithmetic Progression 6, 10, 14, ....?


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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