Question

Question 1 (iv)
Find the sum of the following APs
(iv) $\frac{1}{15},\frac{1}{12},\frac{1}{10},\dots \dots ,to11terms$

Answer 1

(iv) $\frac{1}{15},\frac{1}{12},\frac{1}{10},\dots \dots ,to11termsForthisA.P.,a=\frac{1}{15}n=11d=a_2-a_1=\frac{1}{12}-\frac{1}{15}\frac{5-4}{60}=\frac{1}{60}{S}_{11}=\frac{11}{2}[2\left(\frac{1}{15}\right)+(11-1\left)\frac{1}{60}\right]=\frac{11}{2}[\frac{2}{15}+\frac{10}{60}]=\frac{11}{2}[\frac{2}{15}+\frac{1}{6}]=\frac{11}{2}\left[\frac{4+5}{30}\right]=\left(\frac{11}{2}\right)\left(\frac{9}{30}\right)=\frac{33}{20}$