Question

 
The sum of n terms of an AP is 8558. If the 15 term is 97 and the 10th term is 32. What is the nth term?
2 points
431
474
644
7612


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Answer 1

Answer:

The sum of n terms of an AP is 8558. If the 15 term is 97 and the 10th term is 32. What is the nth term?

2 points

431

474

644

7612

answer 7163

Answer 2

Given :- The sum of n terms of an AP is 8558. If the 15 term is 97 and the 10th term is 32. What is the nth term ?

431

474

644

7612

Solution :-

Let first term of AP is a and common difference is d .

so,

→ T(n) = a + (n - 1)d

given that,

→ T(15) = 97

→ T(10) = 32

then,

→ a + (15 - 1)d = 97

→ a + 14d = 97 ------ Eqn.(1)

and,

→ a + (10 - 1)d = 32

→ a + 9d = 32 ------ Eqn.(2)

subtracting Eqn.(2) from Eqn.(1) we get,

→ a - a + 14d - 9d = 97 - 32

→ 5d = 65

→ d = 13

putting value of d in Eqn.(2),

→ a + 9*13 = 32

→ a = 32 - 117

→ a = (-85)

now,

→ S(n) = (n/2)[2a + (n - 1)d]

→ (n/2)[2a + (n - 1)d] = 8558

→ (n/2)[2* (-85) * (n - 1)13] = 8558

→ (n/2)[-170 + 13n - 13] = 8558

→ n(-183 + 13n) = 17116

→ 13n² - 183n - 17116 = 0

→ 13n² - 572n + 389n - 17116 = 0

→ 13n(n - 44) + 389(n - 44) = 0

→ (13n + 389)(n - 44) = 0

→ n = (-389/13) , 44 .

therefore,

→ T(44) = a + 43d

→ T(44) = (-85) + 43 * 13

→ T(44) = (-85) + 559

→ T(44) = 474 (Ans.)

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