Answer to Question #90346 in Algebra for Michael

Question

1. If the sum of the first 20 terms of an A.P is 200, and the first term is 40, find the common difference.

2. Find the sum to infinity of a G.P whose first term is 2 and common ratio is 19/20

3. Find the sum of the first 10 terms of a G.P whose first term is 5 and the common ratio is 2

Answer 1

1) $S_n=\frac{n(2a+(n-1)d)n}{2}. \;\;S_{20}=\frac{(80+19d)*20}{2}=200.$

So, $d=\frac{20-80}{19}=-\frac{60}{19}.$

2) $S=\frac{a}{1-r}=\frac{2}{1-\frac{19}{20}}=40.$

3) $S_n=\frac{a(1-r^n)}{1-r}.$

$S_{10}=\frac{5(1-2^{10})}{1-2}=5115.$