Question

Find the sum of the following $AP$
(I) $2,7,12$ . To $10$ terms
(II) $1/15,1/12,1/10$ to $11$ terms.

Answer 1

(I) $2,7,\mathrm{12........}$ up to 10 terms

$a=2,d=7-2=5$

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$=\frac{10}{2}\left[2\right(2)+(10-1\left)5\right]$

$=5[4+9\times 5]$

$=5\times 49$

$=245$

(II) $\frac{1}{15},\frac{1}{12},\frac{1}{10},.......$ up to 11 terms

$a=\frac{1}{15},d=\frac{1}{12}-\frac{1}{15}=\frac{1}{60}$

$S_{11}=\frac{11}{2}[2\times \frac{1}{15}+10\times \frac{1}{60}]$

$=\frac{11}{2}[\frac{2}{15}+\frac{1}{6}]$

$=\frac{11}{2}\times \frac{3}{10}$

$=\frac{33}{20}$