Question

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

Answer 1

Answer:

The sum of the first 50 is 5200

Step-by-step 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:

$S_n = \frac{n}{2}[2a + (n-1)*d]$

Where:

$n = 50$

$a = T_1 = 6$

$d = 4$

So:

$S_{50} = \frac{50}{2}[2*6 + (50-1)*4]$

$S_{50} = 25*[12 + 49*4]$

$S_{50} = 25*[12 + 196]$

$S_{50} = 25*208$

$S_{50} = 5200$