Question

If 7^th and 13^th term of an A.P. be 34 and 64 respectively, then its 18^th term is

• A. 87
• B. 88
• C. 89
• D. 90

Answer 1

Answer: (C)

89

Answer 2

Let a be the first term and d be the common difference of the given A.P., then

$T_{7} = 34$ ⇒ $a + 6d = 34$

$T_{13} = 64$ ⇒ $a + 12d = 64$

From (i) and (ii), d = 5, a = 4

∴ $T_{18} = a + 17d = 4 + 17 \times 5 = 89$

Trick: $\frac{T_{n} - T_{k}}{n - k} = \frac{T_{p} - T_{k}}{p - k}$⇒$\frac{T_{18} - T_{7}}{18 - 7} = \frac{T_{13} - T_{7}}{13 - 7}$

⇒ $\frac{T_{18} - 34}{11} = \frac{64 - 34}{6}$

⇒ $T_{18} = 89$