Question

the first term of an arithmetic progression is unity and the common difference is 4 .what will be the term of the AP.

a.4551 ,b.10091,c.7881,d.13531

Answer 1

Given,  a = 1, d = 4. Option 1 : T = 4551 a + (n-1)d = 4551 1 + (n-1)4 = 4551 n-1=4550/4 = not divisible by  4 Option 2 : T = 10091 n-1 = 10090/4 = not divisible by 4 Option 3 : T=7881 n-1 = 7880/4 = 1970 n = 1971 which is an integer.  Therefore Option 3 is correct.

Answer 2

Given,

The first term of an arithmetic progression is unity and the common difference is 4.

To find,

What will be the term of the AP?

Solution,

If the term is in arithmetic progression then an = a + (n-1)d.

a = first term of the arithmetic progression and n is the number of terms in arithmetic progression, and is the nth term and d is a common difference.

a= 1 d =4

(a)   an = 4551.

      4551 = 1 +(n-1)4

      4551-5 = 4n-4

      4550 = 4n - 4

      4554 = 4n

Since 4554 is not divisible by 4 therefore 4551 is not the term of the AP.

(b)    an = 10091

       10091 = 1 +(n-1)4

       10091-1 = 4n-4

       10090 = 4n - 4

       10094= 4n

Since 10094 is divisible by 4 therefore 10091 is the term of the AP.

(c)     an = 7881.

        7881 = 1 +(n-1)4

        7881-1 = 4n-4

        7880 = 4n - 4

        7884 = 4n

Since 7884 is divisible by 4 therefore 7881 is the term of the AP.

(d)     an = 13531.

        13531 = 1 +(n-1)4

        13531-1 = 4n-4

        13530 = 4n - 4

       13534= 4n

Since 13534 is not divisible by 4 therefore 13531 is not the term of the AP.

Hence, 10091 and 7881 are the term of the AP. option(B)and option(C)