Question

Which term of $37,32,27,.....$is $-103?$

Answer 1

Use formula for $n^{th}$term of an A.P

Given sequence is

$37,32,27,.....$

$\Rightarrow a=37,d=32-37=-5$

Let $t_n=-103$

So, applying $t_n=a+(n-1)d$, we get

$-103=37+(n-1)(-5)$

$\Rightarrow -103=37-5n+5$

$\Rightarrow 5n=145$

$\Rightarrow n=29$

Hence, the ${29}^{th}$ term of the sequence is $-103.$