Q8 of 202 Page 9

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.

10a₁₀ = 15a₁₅

10[a + (10 – 1)d] = 15[a + (15 – 1)d]

2a + 2(9)d = 3a + 3(14)d

-a = 42d – 18d

-a = 24d

a = -24d

a₂₅ = a + 24d

= -24d + 24d

= 0

The 6^th and 17^th terms of an A.P. are 19 and 41 respectively, find the 40^th term.

If 9^th term of an A.P. is zero, prove that its 29^th term is double the 19^th term.

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

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.

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