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If the $n t h$ term of an A.P. is $9 − 5 n$ , then the sum of $15$ terms from the following options is:

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450

-450

-465

465

answer is C.

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Detailed Solution

Given that, the

n t h

term of an A.P. is

9 − 5 n

.
Take values for

n

from

1, 2, 3...

and substitute in

9 − 5 n

to formulate the sequence.
For

n = 1

a 1 = 9 − 51 ⇒ a 1 = 4

Therefore the first term is,

a = 4

.
For

n = 2

a 2 = 9 − 52 ⇒ a 2 = − 1

Therefore the second term is,

a 2 = − 1

For

n = 3

a 3 = 9 − 53 ⇒ a 3 = − 6

Therefore the third term is,

a 3 = − 6

Thus the arithmetic progression is,

4, − 1, − 6, ...

.
Substitute

a = 4, d = − 5, n = 15

in the equation

S n = n 2 2 a + n − 1 d

to calculate the sum.

S 15 = 152 24 + 15 − 1 − 5 ⇒ S 15 = 152 8 − 70 ⇒ S 15 = 152 − 62 ⇒ S 15 = − 465

The sum of the 15 terms is -465.
Hence, option 3) is correct.

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