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# How do I find the first term of an arithmetic sequence if the partial term is 51.7, n = 22, and the nth term is -11.3?

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- PuzzlingLv 71 month ago
Partial term? I assume you mean partial *sum*.

The method is just like your last question:

S[n] = n/2(a[1] + a[n])

S[22] = 22/2(a[1] + -11.3) = 51.7

11(a[1] - 11.3) = 51.7

a[1] - 11.3 = 51.7/11

a[1] - 11.3 = 4.7

a[1] = 4.7 + 11.3

a[1] = 16

Answer:The first term is 16

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