If the sum of n terms of an A.P. is (pn | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question: If the sum of n terms of an A.P. is (pn + qn2), where p and q are constants, find the common difference
Answer:

It is known that,

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

According to the given condition,

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

\begin{align}   ⇒ \frac{n}{2}\left[2a + nd-d\right] = pn + qn^2 \end{align}

\begin{align}   ⇒ na + n^2\frac{d}{2} - n.\frac{d}{2}= pn + qn^2 \end{align}

Comparing the coefficients of n2 on both sides, we obtain

\begin{align}   \frac{d}{2} = q \end{align}

\begin{align}  \therefore d = 2q \end{align}

Thus, the common difference of the A.P. is 2q.

 


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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 8: If the sum of n terms of an A.P. is (pn + qn2), where p and q are constants, find the common differe....