Login/Sign Up
Home » 10. In a certain A.P. the term is twice the term. Prove that the term is twice the term.
10. In a certain A.P. the {{24}^{th}} term is twice the {{10}^{ht}} term. Prove that the {{72}^{nd}} term is twice the {{34}^{th}} term.
Arithmetic Progression | Class 10 | ICSE | Maths | RD Sharma
10. In a certain A.P. the {{24}^{th}} term is twice the {{10}^{ht}} term. Prove that the {{72}^{nd}} term is twice the {{34}^{th}} term.

An arithmetic progression or arithmetic sequence is a number’s sequence such that the difference between the consecutive terms is constant.

Solutions:

Given,

{{24}^{th}} term is twice the {{10}^{th}} term.

We know that, {{n}^{th}} term {{a}_{n}}=a+\left( n-1 \right)d

⇒ {{a}_{24}}=2\left( {{a}_{10}} \right)

a+\left( 24-1 \right)d=2\left( a+\left( 10-1 \right)d \right)

a+23d=2\left( a+9d \right)

a+23d=2a+18d

a=5d…. \left( 1 \right)

Now, the {{72}^{nd}}term can be expressed as

{{a}_{72}}=a+\left( 72-1 \right)d

=a+71d

=a+5d+66d

=a+a+66d [using \left( 1 \right)]

=2\left( a+33d \right)

=2\left( a+\left( 34-1 \right)d \right)

=2\left( {{a}_{34}} \right)

⇒ {{a}_{72}}=2\left( {{a}_{34}} \right)

Hence, the {{72}^{nd}} term is twice the {{34}^{th}} term of the given A.P.

i

More Material