Question

Use a formula to find the sum of the first 10 terms

Answer 1

The sum of the first nth terms of a geometric sequence is given by:

`S_n=(a(1-r^n))/(1-r)`

where a is the first term and r is the common ratio.

We know the geometric series is given by:

`a_n=3(2)\placeholder{⬚}^(n-1)`

which means that the first term is 3 and the common ratio is 2. Since we want to know the sum of the first nth terms this means that n=10; plugging these values in the expression for the sum we have:

`\begin{gathered} S_(10)=(3(1-2^(10)))/(1-2) \\ S_(10)=3069 \end{gathered}`

Therefore, the sum we are looking for is 3069