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:

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

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.