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klio [65]
3 years ago
14

Find the first term, a1, of an arithmetic sequence if a15 = 136 and a19 = 168.

Mathematics
1 answer:
Likurg_2 [28]3 years ago
4 0
Since a_n is an arithmetic sequence, there is some constant d by which consecutive terms differ. This means

a_{16}=a_{15}+d
a_{17}=a_{16}+d=a_{15}+2d
a_{18}=a_{17}+d=a_{15}+3d
a_{19}=a_{18}+d=a_{15}+4d

168=136+4d\implies d=8

By a similar token, we can express a_{15} in terms of a_1:

a_2=a_1+d
a_3=a_2+d=a_1+2d
\cdots
a_{15}=a_{14}+d=a_1+14d

136=a_1+14\cdot8\implies a_1=24
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