Question

First 100 terms of the following sequence 3 ,7 ,11

Answer 1

Given that
`a_1 = 3, d = 4`

Find the nth term:


`a_n = 3 + 4(n - 1)`


`a_n = 3 + 4n - 4`


`a_n = 4n - 1`

Find the 100th term:


`a_(100) = 4(100) - 1 = 399`

Find the Sum:


`\text{Sum} = 100((a_1 + a_(100))/(2) )= 100 ((3 + 399)/(2)) = 20100`

Answer 2

Comment
Quick Answer: 20100
I'm going to guess and say you want the sum of the first hundred terms of this series.

Givens
a1 = 3
n = 100
d = 4

Step One
Find L
L = a1 + (n - 1)*d
L = 3 + (100 - 1)*4
L = 3 + 99 * 4
L = 399

Step 2
Find the sum of the first 100 terms of the series.

Sum = (a + L)*n/2

Givens
a = 3
L = 399
n = 100

Sum = (3 + 399)*100/2
Sum = 402 * 50
Sum = 20100 <<<<< Answer

Please leave a note if I am incorrect.