Question 7

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

Answer

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

*k*th term = *a*_{k} = *a *+ (*k* – 1)*d*

∴ *a *+ (*k* – 1)*d* = 5*k* + 1

*a* + *kd* – *d* = 5*k* + 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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Amit Singh chahar
2018-03-13 11:13:28

How the compare the coefficient of k.

Milan
2015-09-28 14:52:52

how do you compare the coefficients in that given question???

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