Home
Class 12
MATHS
If the sum of m consecutive odd integers...

If the sum of m consecutive odd integers is `m^(4)` , then the first integer is

A

`m^(3)+m+1`

B

`m^(3)+m-1`

C

`m^(3)-m-1`

D

`m^(3)-m+1`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `2a+1,2a+3,2a+5,"...."` be the AP, then
`m^(4)=(2a+1)+(2a+3)+(2a+5)+"...."" upto n terms "`
`(m)/(2)={2(2a+1)+(m-1)*2}=m(2a+1+m-1)`
`implies (m)^(3)=(2a+1)+m-1`
`:.2a+1=m^(3)-m+1`
Promotional Banner

Similar Questions

Explore conceptually related problems

IF the sum of three consecutive terms of an A.P. is 21, then first the first term.

If (1+3+5+..+p)+(1+3+5+..+q)=(1+3+5+..+r) where each set of parentheses contains the sum of consecutive odd integers as shown, the smallest possible value of p+q+r(where p >6 ) is a. 12 b. 21 c. 45 d. 54

The product of two consecutive odd numbers is 99.

Show that the square of any positive odd integer is of the form 4q + 1 for any integer q.

Three consecutive integers add up to 51.What are these integers?

Represent the following situations in the form of quadratic equations : The product of two consecutive positive integers is 306. We need to find the Integers.

If the product of two consecutive integers is 306, write its quadratic representation.

Consecutive odd integers whose sum is 25^2-11^2 are

If the roots of x^2-b x+c=0 are two consecutive integers, then b^2-4c is

Find the sum of odd integers from 1 to 2001.