Q7 of 202 Page 9

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

a₉ = 0

a + (9 – 1)d =0

a + 8d = 0

a = -8d …(i)

To Prove: a₂₉ = 2a₁₉

Proof: LHS= a₂₉ = a + 28d = -8d + 28d = 20d

RHS= 2a₁₉ = 2[a + (18)d] = 2(-8d + 18d) = 2(10d) = 20d

Since, LHS=RHS

Hence, proved

The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.

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

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