Test Index

Sequence and Series

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Question : 54 of 86

Marks: +1, -0

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

6
12
6 or 12
None

Solution:

Concept:

Sum of

n

terms of an AP:

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

.

Explanation:

Given: first term

a = 17

, common difference

d = -2

, sum

S_n = 72

.

Substitute into formula:

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

.

Simplify:

72 = \frac{n}{2} [34 - 2n + 2] = \frac{n}{2} [36 - 2n] = n(18 - n)

.

So

n(18 - n) = 72 \Rightarrow 18n - n^2 = 72 \Rightarrow n^2 - 18n + 72 = 0

.

Factor:

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

or

n = 12

.

Answer:

6 or 12

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