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Class 11
Mathematics
Sequence and Series
find the sum to n terms of the a p whose kth ter...

Question: Find the sum to n terms of the A.P., whose kth term is 5k + 1.

Answer:

It is given that the kth term of the A.P. is 5k + 1.

kth term = a_k = a + (k – 1)d

∴ a + (k – 1)d = 5k + 1

a + kd – d = 5k + 1

Comparing the coefficient of k, we obtain d = 5

a – d = 1

⇒ a – 5 = 1

⇒ a = 6

\begin{align} S_n = \frac{n}{2}\left[2a + (n-1)d\right] \end{align}

\begin{align} = \frac{n}{2}\left[2(6) + (n-1)(5)\right] \end{align}

\begin{align} = \frac{n}{2}\left[12 + 5n -5\right] \end{align}

\begin{align} = \frac{n}{2}\left(5n + 7\right) \end{align}

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Question: Find the sum to n terms of the A.P., whose kth term is 5k + 1.

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