Q41 of 202 Page 9

The 24^th term of an A.P. is twice its 10^th term. Show that its 72^nd term is 4 times its 15^th term.

Given: a₂₄=2a₁₀

a +23d= 2(a +9d)

5d=a (i)

To Prove:a₇₂ =4a₁₅

Proof: L.H.S. =a₇₂

= a +71d

=5d +71d [from (i)]

=76d

R.H.S= 4a₁₅

=4(a +14d)

=4a +56d

=4(5d) +56d [from (i)]

=20d +56d

=76d

Since, L.H.S=R.H.S.

Hence proved

The 19^th term of an A.P. is equal to three times its sixth term. If its 9^th term is 19, find the A.P.

The 9^th term of an A.P. is equal to 6 times its second term. If its 5^th term is 22, find the A.P.

Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

If the seventh term of an A.P. is 1/9 and its ninth term is1/7, find its (63)^rd term.

The 24th term of an A.P. is twice its 10th term. Show that its 72nd term is 4 times its 15th term.