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dusya [7]
3 years ago
12

Will give 25 points and brainliest answer if correct

Mathematics
1 answer:
Norma-Jean [14]3 years ago
5 0
Let d be the common difference between terms in the sequence \{a_n\}_{n\ge1}. Then

a_{19}=-58
a_{20}=a_{19}+d
a_{21}=a_{19}+2d
\implies-164=-58+2d\implies d=-53

The first term in the sequence, a_1, satisfies

a_2=a_1+d
a_3=a_1+2d
a_4=a_1+3d
...
a_{19}=a_1+18d
\implies-58=a_1+18(-53)\implies a_1=896

So the explicit formula for the n-th term in the sequence is

a_n=a_1+(n-1)d\implies a_n=896-53(n-1)
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