Question

4. Use the formula to evaluate the series 3 + 6 + 12 + 24 +48 +96. Sn a₁(1 - r^) 1-r​

Answer 1

`S_6=189`

Explanation:

This is a geometric series with
`a_1=3` and common ratio
`r=2`. Using the formula
`\displaystyle S_n=(a_1(1-r^n))/(1-r)` to find the sum of the first
`n=6` terms, we have:

`\displaystyle S_n=(a_1(1-r^n))/(1-r)\\\\S_6=(3(1-2^6))/(1-2)\\\\S_6=(3(1-64))/(-1)\\\\S_6=(3(-63))/(-1)\\\\S_6=(-189)/(-1)\\\\S_6=189`

So, the given series works out to be
`S_6=189`.