Question

Find the sum of the first 33 terms of the arithmetic sequence whose first term is 3 and whose 33rd term is -253.

Answer 1

If you are working on arithmetic sequence, I assume you know this equation.

x = a + d(n-1)

Okay, so the first thing to do is to find the common difference.

-253 = 3 + d(33-1)

Solve for "d" and you get

d = -8

Next, I also assume you know the equation for the sum of an arithmetic sequence.

(n/2)(2a + (n-1)d)

So, plug the numbers in the equation and...

sum = (33/2)(2 x 3 - 8(33-1))
sum = -4125

Answer 2

given:
a = 3
term(33) = a+32d = -253
32d = -256
d = -8

sum(33) = (33/2)(first + last)
= (33/2)(3 -253) = -4125