Question

lf 7th and 13th term of an A. P. are 34 and 64 respectively, then it 18th term is

Answer 1

I hope you understand

Answer 2

Assumption

First term be p

Common difference be d

Given :  

p7 = 34,  p13 = 64

Using the formula we have,

nth term ,

pn = p + (n - 1)d

p7 = p + (7 -  1)d

34 = p + 6d …………..(1)

Also,

p13  = p + (13 - 1)d

64 = p + 12d …………..(2)

Subtracting equation (1) from (2)

(p + 12d) - (p + 6d)  = 64 - 34

p + 12d - p - 6d  = 30

p - p + 12d - 6d = 30

6d = 30

$d=\frac{30}{6}$

d = 5

Now,

Putting the value of d in (1)

34 = p + 6d

34 = p + 6 × 5  

34 = p + 30

p = 34 - 30

p = 4

First term,

p = 4  

Now,

18th term :  

pn = a + (n - 1)d

p18 = 4 + (18 - 1)5

p18 = 4 + 17 × 5

p18 = 4 + 85

p18 = 89

Therefore ,

18th term is 89.