Question

Identify the 42nd term of an arithmetic sequence where a1 = –12 and a27 = 66.
al=1st term, a27=27th term.

Answer 1

General term of an arithmetic sequence for nth term is\[a_n = a_1+d(n-1)\]where d is the common difference.
\[a_{27} = 66\]\[a_{27} =-12+d(27-1)=66\]\[∴d=3\]Now use the general term to find the 42nd term\[a_{42}=-12+3(42-1)=111\]
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