Question

Find the sum of the first 50 terms of the sequence below.
An = 3n + 2

Answer 1

3925

Explanation:

this arithmetic sequence the first term is : A1 = 3(1)+2=5

and common difference is r = 3

the sum of the first 50 terms is : S50 = 50/2(A1 + A50)

A50 = 3(50)+2 = 152

S50 = 50/2(5 + 152)= 3925

Answer 2

An+1= 3n+3 +2
An+1 - An = 3n+5 -3n-2=3
An is aa arithmetic sequence
its sum is given by:
A0 +A1 +A2 + . . . + An = N(Ao + An) /2
where N = n-0=n
S50= A0 +A1 +A2 + . . . + A50 = 50(Ao + A50) /2

S50 = 50(Ao + A50) /2
Ao=2, A50=150+2=152
S50= 50(Ao + A50) /2

finally
S50=25*154=3850