Question

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

Answer 1

a = 150

Explanation:

Sum to infinity of a geometric series

`S_(\infty)=(a)/(1-r)\:\textsf{ for }|r| < 1`

where:

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

Given:

• 
  `S_(\infty)=100`

• 
  `r=-(1)/(2)`

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

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