Q10 of 202 Page 9

In a certain A.P. the 24^th term is twice the 10^th term. Prove that the 72^nd term is twice the 34^th term.

Given: a₂₄ = 2a₁₀

To Prove: a₇₂ = 2a₃₄

Proof: a₂₄ = 2a₁₀

a + (24 –1)d = 2a + 2(10 –1)d

23d – 18d = a

a = 5d

LHS= a₇₂ =a + 71d =5d +71d =76d

RHS= a₃₄ =2a + 2(33)d =10d + 66d =76d

Since, LHS=RHS

Hence, proved

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

The 10^th and 18^th terms of an A.P. are 41 and 73 respectively. Find 26^th term.

If (m+1)^th term of an A.P. is twice the (n+1)^th term, prove that (3m+1)^th term is twice (m+n+1)^th term.

If the n^th term of the A.P.is same as the n^th term of the A.P.find n.

In a certain A.P. the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term.