Question

PLEASE HELP

Which expression defines the arithmetic series 1 + 5 + 9 + ... for seven terms?
Σ(27-1)
Σ(3n-4)
Σ(4n-3)
Σ(n-1)

Answer 1

`\sum\limits^7_(n=1)(4n - 3)`

Explanation:

Given

`1 + 5 + 9 + .....`

Required

Write a definition

First, we derive a formula for the series using:

`T_n = a + (n - 1)d`

From the attached data;

`a = 1`

`d = 5 - 1 = 4`

So:

`T_n = a + (n - 1)d`

`T_n = 1 + (n - 1) * 4`

`T_n = 1 + 4n - 4`

Collect like terms

`T_n = 4n - 4+1`

`T_n = 4n -3`

So, the definition for first 7 terms is:

`\sum\limits^7_(n=1)(4n - 3)`