Question

the sum of the first four terms of an A.P. is 56 the sum of the last four terms is 112 if its first term is 11 then find the number of terms.

Answer 1

$a=11$

sum of first $4$ terms $=56$

$\frac{4}{2}[2a+(n-1\left)d\right]=56\Rightarrow 2[2\times 11+3d]=56\Rightarrow 22+3d=28\Rightarrow 3d=6\Rightarrow d=2$

Sum of last $4$ terms $=112$

$\frac{4}{2}[2\times 12+(n-4+1\left)d\right]=112\Rightarrow 2[22+(n-3\left)d\right]=112\Rightarrow 22+(n-3)\times 2=56\Rightarrow (n-3)2=34n-3=17\Rightarrow n=20$

$\therefore$ no. of terms $=20$