Class 11 Mathematics - Chapter Sequence and Series NCERT Solutions | In an A.P, the first term is 2 and the s
In an A.P, the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is –112.
First term = 2
Let d be the common difference of the A.P.
Therefore, the A.P. is 2, 2 + d, 2 + 2d, 2 + 3d, …
Sum of first five terms = 10 + 10d
Sum of next five terms = 10 + 35d
According to the given condition,
\begin{align} => 10 + 10d = \frac{1}{4}(10 + 35d) \end{align}
\begin{align} => 40 + 40d = 10 + 35d \end{align}
\begin{align} => 30 = - 5d \end{align}
\begin{align} => d = - 6 \end{align}
\begin{align} \therefore a_{20} = a + (20 -1)d = 2 + (19)(-6) = 2 - 114 = -112\end{align}
Thus, the 20th term of the A.P. is –112.
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