Question

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

• A. 144
• B. 1
• C. 0
• D. 8

Answer 1

The correct option is C 0

Given,
$8a_8=15a_{15}.$
Since the $n^{\text{th}}$ term of an AP of first term $a$ and common difference $d$ is given by
$a_n=a+(n-1)d,$ we have

$8[a+(8-1\left)d\right]=15[a+(15-1\left)d\right].\Rightarrow 8(a+7d)=15(a+14d)\Rightarrow 8a+56d=15a+210d\Rightarrow 7a+154d=0\Rightarrow a+22d=0\Rightarrow a+(23-1)d=0$
Hence, the ${23}^{\text{rd}}$ term of the AP is zero.