Math, asked by SanyaGirdhar7499, 1 year ago

how many terms of the AP 72,69,66,..make the sum 897 ?

Answers

Answered by abhinash49
25
Hey mate here is your solution ...number of terms will be 23 ....
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Answered by wifilethbridge
6

Given :

AP:72,69,66,..

To Find:

how many terms of the AP 72,69,66,..make the sum 897 ?

Solution:

AP:72,69,66,..

First term = a = 72

Common difference = d = 69-72=66-69=-3

Formula of sum of first n terms :

S_n=\frac{n}{2}(2a+(n-1)d)

We are supposed to find how many terms of the AP 72,69,66,..make the sum 897 ?

So,897=\frac{n}{2}(2(72)+(n-1)(-3))\\897 \times 2 =(144-3n+3)n\\1794=147n-3n^2\\598=49n-n^2\\n^2-49n+598=0\\n^2-26n-23n+598\\n(n-26)-23(n-26)=0\\(n-23)(n-26)=0

n= 23,26

Since the sum of 23 terms is equal to the sum of 26 terms

So, 23  terms of the AP 72,69,66,..make the sum 897

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