SOLUTION: the first three terms of an arithmetic progression are a1=576 a2=599 a3=622 find the tenth term, a10 and the sum of the first ten terms

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Question 355683: the first three terms of an arithmetic progression are
a1=576 a2=599 a3=622
find the tenth term, a10 and the sum of the first ten terms
Found 2 solutions by ewatrrr, Fombitz:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
*Note: For an Arithmetic progression
a%5Bn%5D+=+a%5B1%5D+%2B+%28n-1%29d and Sum%5Bn%5D+=+%28n%28a%5B1%5D+%2B+a%5Bn%5D%29%29%2F2
.
d = 23
a%5B10%5D+=+576+%2B+9%2A23+=+783+
.
Sum%5Bn%5D+=+%28n%28a%5B1%5D+%2B+a%5Bn%5D%29%29%2F2
.
Sum%5B10%5D+=+%2810%2A%28576+%2B+783+%29%29%2F2

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
d=a2-a1=599-576=23
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.
.
a%28n%29=576%2B%28n-1%29%2Ad
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.
a%2810%29=576%2B%2810-1%29%2A23
a%2810%29=576%2B9%2A23
a%2810%29=576%2B207
highlight%28a%2810%29=783%29
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.
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S%28n%29=%28n%28a%281%29%2Ba%28n%29%29%29%2F2
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S%2810%29=%2810%28a%281%29%2Ba%2810%29%29%29%2F2
S%2810%29=5%28576%2B783%29
highlight%28S%2810%29=6795%29