Q. 174.8( 8 Votes )

# The sum of three numbers in A.P. is 12, and the sum of their cubes is 288. Find the numbers.

Answer :

assume the numbers in AP are a - d, a, a + d

**Given** that the sum of three numbers is 12

**To find**: the first three terms of AP

So,

3a = 12

a = 4

It is also given that the sum of their cube is 288

(a - d)^{3} + a^{3} + (a + d)^{3} = 288

a^{3} - d^{3} - 3ad(a - d) + a^{3} + a^{3} + d^{3} + 3ad(a + d) = 288

substituting a = 4 we get

64 - d^{3} - 12d(4 - d) + 64 + 64 + d^{3} + 12d(4 + d) = 288

192 + 24d^{2} = 288

d = 2 or d = - 2

hence the numbers are a - d, a, a + d which is 2, 4, 6 or 6, 4, 2

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