Question

The first term of an arithmetic sequence is −12 . The common difference of the sequence is 7. What is the sum of the first 30 terms of the sequence? Enter your answer in the box.

Answer 1

Answer:

2685

Step-by-step explanation:

The nth term of an arithmetic sequence is:

aₙ = a₁ + d (n − 1)

where a₁ is the first term and d is the common difference.

Here, a₁ = -12 and d = 7:

aₙ = -12 + 7 (n − 1)

aₙ = -12 + 7n − 7

aₙ = -19 + 7n

The sum of the first n terms of an arithmetic sequence is:

S = (n/2) (a₁ + aₙ)

First, we find the 30th term:

a₃₀ = -19 + 7(30)

a₃₀ = 191

Now we find the sum:

S = (30/2) (-12 + 191)

S = 2685