Question -
Answer -
(i) Is 68 a term of theA.P. 7, 10, 13,…?
Given A.P is 7, 10,13,…
Here, a1 =a = 7, a2 = 10
Common difference, d =a2 – a1 = 10 – 7 = 3
We know, an =a + (n – 1)d [where, a is first term or a1 and d is commondifference and n is any natural number]
an = 7+ (n – 1)3
= 7 + 3n – 3
= 3n + 4
Now, to find whether68 is a term of this A.P. or not
Put an =68
3n + 4 = 68
3n = 68 – 4
3n = 64
n = 64/3
64/3 is not anatural number
Hence, 68 is not aterm of given A.P.
(ii) Is 302 a term of theA.P. 3, 8, 13,…?
Given A.P is 3, 8,13,…
Here, a1 =a = 3, a2 = 8
Common difference, d =a2 – a1 = 8 – 3 = 5
We know, an =a + (n – 1)d
an = 3+ (n – 1)5
= 3 + 5n – 5
= 5n – 2
To find whether 302 isa term of this A.P. or not
Put an =302
5n – 2 = 302
5n = 302 + 2
5n = 304
n = 304/5
304/5 is not anatural number
Hence, 304 is not aterm of given A.P.