Question

If the first 4 terms of an infinite geometric sequence are 150, 120, 96, and 76. & then the sum of all theterms in the sequence is

Answer 1

Consider the given geometric sequence,

`150,120,96,76.8,\ldots\ldots\ldots`

Here, the first term (a) and common ratio (r) are,

`\begin{gathered} a=150 \\ r=(120)/(150)=0.8 \end{gathered}`

Consider that the sum of an infinite geometric sequence is given by,

`S=(a)/(1-r)`

Substitute the values and simplify,

`\begin{gathered} S=(150)/(1-0.8) \\ S=(150)/(0.2) \\ S=750 \end{gathered}`

Thus, the sum of the given infinite geometric sequence is 750 .