An arithmetic progression 5,12,19.....has 50 terms.Find its last term.Hence find the sum of its last 15 terms.

Given,AP is $5,12,\mathrm{19....}$

Here,$n=50,a=5,d=7$

nth term of AP given as

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

Now, $T_{50}=a+(50-1)d$

$\Rightarrow T_{50}=5+\left(49\right)7=348$

15th terms from last$=(50-15+1)$ terms from starting

$T_{36}=a+(36-1)d$

$=5+35\left(7\right)$

$=250$

$\therefore$ Sum of last 15 terms

=$\frac{n}{2}(a+l)$

=$\frac{15}{2}(250+348)$

$[\because a=250andl=348]$

=$\frac{15}{2}\times 598$

=4485