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UPSC NDA II 2024 Mathematics Paper

Question Numbers: 43-44

Direction : Consider the following for the items that follow :

The product of 5 consecutive terms of an AP is 229635. The first, second and fifth terms are in GP.

Question : 44 of 120

Marks: +1, -0

What is the sum of all five terms?

Solution:

Concept:

This problem involves an arithmetic progression (AP) of five terms. The middle term is

a

and the common difference is

d

Explanation:

From the given condition, we obtain

5 \times 6 = 2a

Solving gives

a = 15

Thus, the five terms are

a-2d

a-d

a

a+d

a+2d

which equal

3,\ 9,\ 15,\ 21,\ 27

Their sum is

3 + 9 + 15 + 21 + 27 = 75

Answer:

75 (Option C)

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