Question

the first term of an a.p. is unity and the common difference is 4 .which among these will be a term of this a.p.-a)4551. b)10091. c)7881 d)13531

Answer 1

first term of Ap=1
common difference=4
hence nth term (tn)=a+(n-1) d
only that number is ppossible in AP which gives integer value of n
now calculate n for each number,

(1) 4551=1+(n-1) d
4550/4=1137.5 =n
hence this is not possible

(2) 10091=1+(n-1) 4
10090/4=2522.5 =n
this is also not possible

(3) 7881=1+(n-1) 4
7880/4=1970=n
n gain integer value so , 7881 is In Ap

(4) 13531=1+(n-1) 4
13530/4=3382.5 =n
this is not possible

hence option (c) is in AP

Answer 2

First term , a = 1
Common difference , d = 4
an = a + (n - 1)d

Now, we have to check every option, the option that gives 'n' as an integer then that is the answer.
Among the four options given,
c) 7881 = a + (n - 1)d
7881 = 1 + (n - 1)4
7881 = 1 + 4n - 4
7884 = 4n
n = 1971
Here n is an integer so 7881 is a term of the given A.P

Therefore (C) is the correct option.