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hram777 [196]
3 years ago
10

An arithmetic sequence is represented in the following table. Enter the missing term of the sequence.

Mathematics
1 answer:
bija089 [108]3 years ago
4 0

a_1=-9\\\\a_2=a_1-8\to a_2=-9-8=-17\\\\a_3=a_2-8\to a_3=-17-8=-25\\\\a_4=a_3-8\to a_4=-25-8=-33\\\\\text{The general term of an arithmetic sequence:}\\\\a_n=a_1+(n-1)d\\\\a_1-first\ term\\d-common\ difference\\\\\text{We have}\ a_1=-9\ \text{and}\ d=-8.\ \text{Substitute:}\\\\a_n=-9+(n-1)(-8)=-9-8n+8=-8n-1\\\\\text{Put n = 43 and calculate}\ a_{43}\\\\a_{43}=-8(43)-1=-344-1=-345\\\\Answer:\ \boxed{?=-345}

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Step-by-step explanation:

There are two consecutive positive even integers such that the square of the first is 364 more than five times a second. What are the two numbers?

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