Question

Identify the 42nd term of an arithmetic sequence where a1=-12 and a27=66.

Answer 1

you need to find the common difference d

using the 27th term

\[T _{27} = -12 + (27 -1)d\]

or \[66 = -12 + 26d\]

solve for d

then evaluate the formula with n = 42

Answer 2

\[a(n) = a(1) + (n - 1)d\]
\[a(1) = -12\]a(n) = -12 + (n - 1)d
\[a(27) = 66\]66 = -12 + (27 - 1)d
\[66 = -12 + 26d\]
\[26d = 66 + 12\]
\[26d = 78\]
\[d = 78/26\]
\[d = 3\]
\[a(n) = -12 + 3(n - 1)\]
\[a(42) = -12 + 3(42 - 1) = -12 + 3(41) = -12 + 123 = 111\]