Question

If $7^{th}$ and ${13}^{th}$ terms of an A.P. are 34 and 64, respectively, then its ${18}^{th}$ term is

• A. $87$
• B. $88$
• C. $89$
• D. $90$

Answer 1

Answer: (C)

$89$

$7^{th}$ term of the A.P. is $=34=a_7$

${13}^{th}$ term of the A.P. is $=64=a_{13}$

Let $a$ be the 1st term $d$ be the common diff.

$\therefore a_7=34$

$\therefore a_7=34$

$\Rightarrow a+6d=34$ ____(i)

again

$a_{13}=64$

$\Rightarrow a+12d=64$ ___(ii)

(ii) - (i)

$\Rightarrow 6d=30$

$\Rightarrow d=5$

$\therefore a=34-6d$

$=34-30$

$=4$

$\therefore a=4$

Now, ${18}^{th}$ term $=a+(18-1)d$

$=a+17d$

$=a+17\times 5$

$=4+17\times 5$

$=4+85$

$=89$

$\therefore a_{18}=89$