If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 1

1.	If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is A. 87 B. 88 C. 89 D. 90
Answer» Option : (C) Here, a₇ = 34 and a₁₃ = 64 i.e., a + 6d = 34 ...(i) And, a +12d = 64 ...(ii) Subtracting (i) from (ii) we get, (12-6) d = 64 - 34 ∴6d = 30 ∴ d = 5 Substituting d = 5 in (i) we get, a+6(5) = 34 ∴a + 30 = 34 ∴ a = 4 Now, 18^th term is given by a₁₈ = a+17d = 4+17×5 = 89

If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is A. 87 B. 88 C. 89 D. 90

Answer»

Option : (C)

Here,

a₇ = 34 and a₁₃ = 64

i.e.,

a + 6d = 34 ...(i)

And,

a +12d = 64 ...(ii)

Subtracting (i) from (ii) we get,

(12-6) d = 64 - 34

∴6d = 30

∴ d = 5

Substituting d = 5 in (i) we get,

a+6(5) = 34

∴a + 30 = 34

∴ a = 4

Now,

18^th term is given by a₁₈ = a+17d

= 4+17×5

= 89