Question

Find the number of terms in each of the following $APs$:
(a)$7,13,19,..205$
(b)$18,15\frac{1}{2},13,..,-47$

Answer 1

$\left(a\right)$

$7,13,19\dots 205.$

$a=7,d=6$

$a_n=a+(n-1)d$

$205=7+(n-1)6$

$n-1=\frac{198}{6}$

$n=33+1=34$

$\left(b\right)$

$18,15\frac{1}{2},13\cdots -47$

$a=18,d=-\frac{5}{2}$

$a_n=a+(n-1)d$

$-47=18+(n-1)(-\frac{5}{2})$

$\frac{5}{2}(n-1)=65$

$(n-1)=26$

$n=27$