Question

The average of 3 consecutive terms of an AP is 18. If the 3rd term is 24 then what is the first term?

Answer 1

Answer:-

$\sf{The \ first \ term \ of \ the \ AP \ is \ 12.}$

Given:

• The average of 3 consecutive terms of an AP is 18.

• The 3rd term is 24 .

To find:

• The first term of the AP.

Solution:

$\sf{Let \ the \ first \ three \ terms \ of \ an \ AP \ be}$

$\sf{(a-d), \ a \ and \ (a+d)}$

$\sf{According \ to \ the \ first \ condition. }$

$\boxed{\sf{Average=\frac{Sum \ of \ observations}{Number \ of \ observations}}}$

$\sf{\therefore{\frac{(a-d)+a+(a+d)}{3}=18}}$

$\sf{\therefore{\frac{3a}{3}=18}}$

$\sf{\therefore{a=18...(1)}}$

$\sf{According \ to \ the \ second \ condition. }$

$\sf{t_{3}=24}$

$\sf{\therefore{a+d=24}}$

$\sf{But, \ here \ a=18 \ from \ (1)}$

$\sf{\therefore{18+d=24}}$

$\sf{\therefore{d=24-18}}$

$\sf{\therefore{d=6}}$

$\sf{Here, \ a=18 \ and \ d=6}$

$\sf{First \ term=a-d=18-6}$

$\sf{\therefore{First \ term(t_{1})=12}}$

$\sf\purple{\tt{\therefore{The \ first \ term \ of \ the \ AP \ is \ 12.}}}$