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In an A.P, the first term is 2 and the sum of the first five terms is ...

In an A.P, the first term is 2 and the s | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question: 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.

Answer:

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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Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 2 , Question 3: In an A.P, the first term is 2 and the sum of the first five terms is one-fourth of the next five te....

In an A.P, the first term is 2 and the s | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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