Question

The ${30}^{th}$ term of the $A.Pseries:10,7,\mathrm{4....}$ is $-b$,
what is the value of $b?$

Answer 1

Consider the given A.P. series

$10,7,\mathrm{4........}$

$a=10$

$d=7-10=-3$

$n=30$

Find $a_{30}$

We know that, $a_n=a+(n-1)d$

$a_{30}=10+(30-1)\times (-3)$

$a_{30}=10-87$

$a_{30}=-77$
Comparing $-b=-77\Rightarrow b=77$

Hence, this is the answer.