Q. 84.0( 98 Votes )

# If the sum of n terms of an A.P. is (pn + qn^{2}), where p and q are constants, find the common difference.

Answer :

**Given: Sum of n terms of A.P. = pn + qn ^{2}**

We know,

a = first term and

d = common difference

Now equating the given Sum with the formula we get,

∴

Comparing the coefficients of n^{2} on both sides, we obtain

⇒ d = 2q

**∴ the common difference of the A.P. is 2q.**

Rate this question :

Find the second term and nth term of an A.P. whose 6^{th} term is 12 and 8^{th} term is 22.

There are n A.M.s between 3 and 17. The ratio of the last mean to the first mean is 3 : 1. Find the value of n.

RD Sharma - MathematicsIf x, y, z are in A.P. and A_{1}is the A.M. of x and y, and A_{2} is the A.M. of y and z, then prove that the A.M. of A_{1} and A_{2} is y.

Insert 7 A.M.s between 2 and 17.

RD Sharma - MathematicsThe 10^{th} and 18^{th} term of an A.P. are 41 and 73 respectively, find 26^{th} term.

If 10 times the 10^{th} term of an A.P. is equal to 15 times the 15^{th} term, show that the 25^{th} term of the A.P. is Zero.

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P

RD Sharma - MathematicsThe 4^{th} term of an A.P. is three times the first and the 7^{th} term exceeds twice the third term by 1. Find the first term and the common difference.

In an A.P. the first term is 2, and the sum of the first 5 terms is one-fourth of the next 5 terms. Show that 20th term is - 112

RD Sharma - MathematicsInsert 4 A.M.s between 4 and 19.

RD Sharma - Mathematics