Question

Find the sum of the following APs:
i) $2,7,12,\dots ,$ to 10 terms
ii)$-37,-33,-29,\dots ,$ to 12 terms
iii)$0.6,1.7,2.8,\dots ,$to 100 terms

Answer 1

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

i)

$a=2$

$d=5$

$n=10$

$S_{10}=\frac{10}{2}(4+(10-1\left)5\right)$

$S_{10}=5(4+(9\left)5\right)$

$S_{10}=5\left(49\right)$

$S_{10}=245$

ii)

$a=-37$

$d=-4$

$n=12$

$S_{12}=\frac{12}{2}(-74+(12-1)-4)$

$S_{12}=6(-74+(11\left)4\right)$

$S_{12}=6(-74+44)$

$S_{12}=6(-30)$

$S_{12}=-180$

iii)

$a=0.6$

$d=1.1$

$n=100$

$S_{100}=\frac{100}{2}(1.2+(100-1\left)1.1\right)$

$S_{100}=50(1.2+(99\left)1.1\right)$

$S_{100}=50(1.2+108.9)$

$S_{100}=50\left(110.1\right)$

$S_{100}=5505$