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