Test Index

Sequence and Series

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Question : 5 of 86

Marks: +1, -0

The sum of a series in A.P. is 72 the first term being 17 and the common difference -2 . the number of terms is

6
12
6 or 12
10

Solution:

Concept:

Sum of

n

terms of an AP:

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

.

Explanation:

Given

a = 17

,

d = -2

,

S_n = 72

.

Substitute:

\frac{n}{2}[2(17) + (n-1)(-2)] = 72

.

Simplify inside:

\frac{n}{2}[34 - 2n + 2] = \frac{n}{2}(36 - 2n) = 72

.

Multiply both sides by 2:

n(36 - 2n) = 144

.

Expand:

36n - 2n^2 = 144

.

Rearrange:

-2n^2 + 36n - 144 = 0

→ divide by

-2

:

n^2 - 18n + 72 = 0

.

Factor:

(n - 6)(n - 12) = 0

, so

n = 6

or

n = 12

.

Answer:

n = 6

or

12

.

Correct option: C (6 or 12).

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