Question

Type the correct answer in each box. If necessary, use / for the fraction bar. Complete the statements about series A and B. Series A: 10+4+8/5+16/25+32/125+⋯ Series B: 15+3/5+9/5+27/5+81/5+⋯ Series__ has an r value of___where 0<|r|<1. So, we can find the sum of the series. The sum of the series is___ need help guys please :/

Answer 1

Answer:

Series A has an r value of 2/5 and series A has an r value of 3. The sum of the series A is 50/3

Step-by-step explanation:

A geometric sequence is in the form a, ar, ar², ar³, .  .   .

Where a is the first term and r is the common ratio = $\frac{a_{n+1}}{a_n}$

For series A:  10+4+8/5+16/25+32/125+⋯   The common ratio r is given as:

$r=\frac{a_{n+1}}{a_n}=\frac{4}{10} =\frac{2}{5}$

For series B: 1/5+3/5+9/5+27/5+81/5+⋯   The common ratio r is given as:

$r=\frac{a_{n+1}}{a_n}=\frac{3/5}{1/5} =3$

For series A a = 10, r = 2/5, which mean 0 < r < 1, the sum of the series is given as:

$S_{\infty}=\frac{a}{1-r}=\frac{10}{1-\frac{2}{5} } =\frac{50}{3}$