Question

In an A.P, the $1^{st}$ term is $4$ and the $9^{th}$ term is $20$. Then the ${15}^{th}$ term will be

• A. $16$
• B. $32$
• C. $18$
• D. $36$

Answer 1

Answer: (B)

$32$

Given

$1^{st}term=4=a_1$

$9^{th}term=20=a_9$

we know, the formula for nth term of an A.P is

$a_n=a_1+(n-1)d$.....(1)

Hence,

$a_9=a_1+(9-1)d$........from (1)

$a_9=a_1+\left(8\right)d$

$20=4+8d$

$16=8d$

$d=2$.

Therefore

$a_{15}=a_1+(15-1)d$

$=a_1+\left(14\right)d$

$=4+14\left(2\right)$

$=28+4$

$=32$.

$\therefore The{15}^{th}termoftheA.P=32$

Hence, the answer is $Opt:\left[B\right]$