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The sum of the first 9 term of an AP is 72 and the sum...

The sum of the first 9 term of an AP is 72 and the sum of the next 4 terms is 71.Find the AP?

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Answers (3)

HENRYVILLA
1 month ago
The first number is x, the second is x+5, the 3rd is x+10, etc. So the sum of the first 9 terms is 9x + (5 + 10 + 15 + etc.) = 9x + 5(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8). Since the sum of the first n positive integers is n(n+1)/2, The sum of the first 9 terms is

9x + 5(8*9/2) = 9x + 180.

So, 9x + 180 = 72. Therefore, x = (72–180)/9 = -12. The 10th term is -12 + 5*9 = 33.
ANTHONY SOLUTION
1 month ago
→ (1)

It is also given that sum of first 20 terms is 400





→ (2)

Subtract (1) from (2)





Put d = 2 in (1), we get

2a + 8(2) = 18

2a = 18 − 16 = 2

∴ a = 1
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