Question

The sum of the first 50 terms of 6,10,14 to the nearest integer.

Answer 1

The sum of the first 50 is 5200

Explanation:

Given

Sequence: 6, 10, 14

Required

Determine the sum of the first 50

The given sequence is a linear sequence.

So, first we calculate the common difference

`d = T_2 - T_1`

`d = 10 - 6 = 4`

The sum of the first 50 terms is then calculated using:

`S_n = (n)/(2)[2a + (n-1)*d]`

Where:

`n = 50`

`a = T_1 = 6`

`d = 4`

So:

`S_(50) = (50)/(2)[2*6 + (50-1)*4]`

`S_(50) = 25*[12 + 49*4]`

`S_(50) = 25*[12 + 196]`

`S_(50) = 25*208`

`S_(50) = 5200`