What is the Sum of the first 50 terms of the sequence below?

The sum of the first n terms of an arithmetic sequence is the sum of the first and last terms, times the number of terms, divided by 2.

We have:

a(n) = 3n + 2

We need the first and last term, so:

a(1) = 3(1) + 2 and a(50) = 3(50) + 2

a(1) = 3 + 2 and a(50) = 150 + 2

a(1) = 5 and a(50) = 152

Now the equation that I mentioned above:

S(n) = [ a(1) + a(n) ] n / 2

With n = 50 we get:

S(50) = [ a(1) + a(50) ] * 50 / 2

S(50) = 25[ a(1) + a(50) ]

Now substitute the values for a(1) and a(50):

S(50) = 25(5 + 152)

S(50) = 25(157)

S(50) = 3925

That's your sum.

an = 3(n) + 2

S50 

= 5 + 8 + 11 + ... + 152

= 25(157) = 3925