Question

Write the summation that represents the series 15 + 18 + 21 + 24. What is the explicit formula for the series shown?

Answer 1

Summation:
`\sum_(n=1)^4(3n+12)`

Explicit formula:
`a_n=3n+12`

Explanation:

The given series is 15 + 18 + 21 + 24.

The first term of this series is
`a_1=15`.

The common difference is
`d=18-15=3`

The explicit formula is given by:
`a_n=a_1+d(n-1)`.

We plug in the known values to get:

`a_n=15+3(n-1)`

`a_n=15+3n-3`

The explicit formula is
`a_n=3n+12`

The summation that represents the series is:
`\sum_(n=1)^4(3n+12)`