(i) Is 68 a term of the A.P. 7, 10, 13,…? (ii) Is 302 a term of the A.P. 3, 8, 13,…?
(i) Is 68 a term of the A.P. 7, 10, 13,…? (ii) Is 302 a term of the A.P. 3, 8, 13,…?

Answers:

(i) 

Given,

A.P is 7, 10, 13,…

a1 = a = 7

a2 = 10

Common difference, d = a2 – a1 = 10 – 7 = 3

an = a + (n – 1)d

an = 7 + (n – 1)3

= 7 + 3n – 3

= 3n + 4

Put, an = 68

3n + 4 = 68

3n = 68 – 4

3n = 64

n = 64/3

64/3 is not a natural number

68 is not a term of given A.P.

(ii) 

Given,

A.P is 3, 8, 13,…

a1 = a = 3

a2 = 8

Common difference, d = a2 – a1 = 8 – 3 = 5

an = a + (n – 1)d

an = 3 + (n – 1)5

= 3 + 5n – 5

= 5n – 2

Put, an = 302

5n – 2 = 302

5n = 302 + 2

5n = 304

n = 304/5

304/5 is not a natural number

304 is not a term of the A.P.