SOLUTION: Find the nth partial sum of the arithmetic sequence. an = 2n − x; n = 19

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Question 1178676: Find the nth partial sum of the arithmetic sequence.
an = 2n − x; n = 19
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+=+2n+-x
n+=+19

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
so, a%5B1%5D%2Bd%28n-1%29=+2n+-x
substitute n+=+19
=>a%5B1%5D%2Bd%2819-1%29+=+2%2A19+-x
=>a%5B1%5D%2B18d=+38+-x
=>a%5B1%5D=++38+-x-18d

go to

S%5Bn%5D=%28n%2F2%29%2A%282a%5B1%5D%2B%28n-1%29d%29.........substitute a%5B1%5D+and n
S%5B19%5D=%2819%2F2%29%2A%282%2838+-x-18d%29%2B%2819-1%29d%29
S%5B19%5D=%2819%2F2%29%2A%2876+-2x-36d%2B18d%29
S%5B19%5D=%2819%2F2%29%2A%28-18+d+-+2+x+%2B+76%29
S%5B19%5D=-171d+-+19x+%2B+722