Algebra 2 help!

Question

What is the sum of the first 51 terms of the sequence?

-282, -266, -250, -234....

S51=

Answer 1

Sum of an arithmetic sequence = n/2 * (2a + (n-1)d), where n = number of terms, a = first term, d = common difference between terms.

Here n = 51, a = -282 and d = 16. Plug those numbers into the formula and you have your answer.

Answer 2

This is arithmetic sequense with a₁ = - 282 and common difference d = - 266 - (- 282) = 16.

Then a₅₁ = a₁ + 50d = - 282 + 50·16 = 518.

Then S₅₁ = 51/2(a₁ + a51) = 51/2(- 282 + 518) = 6018