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

Given:

The 7th term of the arithmetic progression (A.P.) = 34

The 13th term of the arithmetic progression (A.P.) = 64

Formula Used:

General term of an A.P. = a + (n - 1) × d

Where,

a = first term

d = common difference

n = term number

Calculation:

The formula for the nth term gives:

7th term = a + (7 - 1) × d = 34

⇒ a + 6d = 34

13th term = a + (13 - 1) × d = 64

⇒ a + 12d = 64

Subtracting the first equation from the second:

(a + 12d) - (a + 6d) = 64 - 34

⇒ 6d = 30

⇒ d = 5

Substitute d = 5 into the first equation:

a + 6 × 5 = 34

⇒ a + 30 = 34

⇒ a = 4

Now, find the 18th term:

18th term = a + (18 - 1) × d

⇒ 18th term = 4 + 17 × 5

⇒ 18th term = 4 + 85

⇒ 18th term = 89

The 18th term of the A.P. is 89.