SOLUTION: Find the nth partial sum of the arithmetic sequence. an = 7n + 2; n = 10

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Question 1178675: Find the nth partial sum of the arithmetic sequence.
an = 7n + 2; n = 10
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find the nth partial sum of the arithmetic sequence.
given:
a%5Bn%5D+=+7n+%2B+2
n+=+10
the nth partial sum formula of the arithmetic sequence:
S%5Bn%5D=%28n%2F2%29%2A%282a%5B1%5D%2B%28n-1%29d%29
find first term:
a%5Bn%5D=a%5B1%5D%2Bd%28n-1%29+=+7n+%2B+2
substitute n+=+10
=>a%5B1%5D%2Bd%2810-1%29+=+7%2A10+%2B+2
=>a%5B1%5D%2B9d=+72
=>a%5B1%5D=+72-9d
go to
S%5Bn%5D=%28n%2F2%29%2A%282a%5B1%5D%2B%28n-1%29d%29.........substitute a%5B1%5D+and n
S%5B10%5D=%2810%2F2%29%2A%282%2872-9d%29%2B%2810-1%29d%29
S%5B10%5D=5%2A%28144-9d%29
S%5B10%5D=720-45d