Question

THE SUM 10 INFINITY OF A GEOMETRIC SERIES IS 100. FIND THE TERM IF THE COMMON FIRST RATIO IS - 1/2​

Answer 1

Answer:

a = 150

Step-by-step explanation:

Sum to infinity of a geometric series

$S_{\infty}=\dfrac{a}{1-r}\:\textsf{ for }|r| < 1$

where:

• a is the first term
• r is the common ratio

Given:

• $S_{\infty}=100$

• $r=-\dfrac{1}{2}$

Substitute the given values into the formula and solve for a:

$\begin{aligned}S_{\infty} & =\dfrac{a}{1-r}\\\\\implies 100 & =\dfrac{a}{1-\left(-\frac{1}{2}\right)}\\\\ 100 & =\dfrac{a}{1+\frac{1}{2}}\\\\100 & = \dfrac{a}{\frac{3}{2}}\\\\a & = \dfrac{3}{2} \cdot 100\\\\a & = 150\end{aligned}$