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 te
rms of the sequence? Enter your answer in the box.
1 answer:
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
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