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201603-12-Q3
The 12th term of an arithmetic progression is 17 and the sum of the first 31 terms is 1023. Find the 31st term. [5]
解题Solution
- The 12th term of an arithmetic progression is 17
$$
a + (12 - 1)d = 17
$$
- the sum of the first 31 terms is 1023
$$
\frac{31}{2}(a + a + (31-1)d) = 1023
$$
- Solve the equation group解方程组
\begin{cases}
& a = -27 \\
& d = 4
\end{cases}
- The 31st term is
$$
-27 + (31 - 1)4 = 93
$$
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