Question

If the sum of first n terms of an A.P is 2m²+3m, then find 3rd term and 11th term. step by step.

Answer 1

sum of n terms=
${2m}^{2} + 3m$
$sum \: of \: 1 \: term \: is \\ m = 1 \\ s1 = 5 \\ sum \: of \: 2 \: terms \: s2 = 2 \times {2}^{2} + 3 \times 2 = 14$
so common difference(d) is s2-s1=14-5=9
$3rd \: term \: is \\ a + (n - 1)d \\ 5 + (3 - 1)9 \\ 5 + 18 = 23$
so 11 th term is
a+(n-1)d
5+(11-1)9
5+90
95

so 3rd term is 23 and 11 term is 95