Test Index

Sequence and Series

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Question : 83 of 86

Marks: +1, -0

If 8 th term of an AP is

15,

the Sum of the 15 its term is

15
0
225
$\frac{225}{2}$

Solution:

Concept:

For an AP, the sum of the first

n

terms is

n

times the middle term when

n

is odd.

Explanation:

Given the 8th term

a + 7d = 15

.

Sum of first 15 terms:

S_{15} = \frac{15}{2}[2a + 14d] = \frac{15}{2} \cdot 2(a+7d) = 15 \times 15 = 225

.

Alternatively, since 15 is odd, the 8th term is the middle term, so

S_{15} = 15 \times 15 = 225

.

Answer:

225

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