If 8 times the 8th term of an AP is equal to 15 times the 15th term

Question -

If 8 times the $8^{th}$ term of an AP is equal to 15 times the $15^{th}$ term of the AP, then the $23^{rd}$ term of the AP is ___.

Options:

A . 144

B . 1

C . 0

D . 8

Answer: Option C
:
C
Given,

8 a_{8} = 15 a_{15} .

Since the

n^{th}

term of an AP of first term

a

and common difference

d

is given by

a_{n} = a + (n - 1) d,

we have

8 [a + (8 - 1) d] = 15 [a + (15 - 1) d] . \Rightarrow 8 (a + 7 d) = 15 (a + 14 d) \Rightarrow 8 a + 56 d = 15 a + 210 d \Rightarrow 7 a + 154 d = 0 \Rightarrow a + 22 d = 0 \Rightarrow a + (23 - 1) d = 0

Hence, the

23^{rd}

term of the AP is zero.

Was this answer helpful ?

Next Question