Question

If 4 and 7 are the 2nd and 3rd terms of an A.P. respectively, then its first term is _______.

Answer 1

a + d = 4 __(1)

a + 2d = 7 ___(2)

Subtracting eq (1) from eq (2):

a + d - a - 2d = 4 - 7

=> d = 3

a = 4 - d [from (1)]

=> a = 1

Answer 2

Given,

The 2nd and 3rd term of the given A.P are 4 and 7, respectively.

To find,

The first term of the given A.P.

Solution,

The common difference between the two consecutive terms of the given A.P

= 3rd term of the A.P - 2nd term of the A.P

= 7-4

= 3

Now,let the first term of the given A.P = x

[Assume,x as a variable to do the further mathematical calculations.]

So,the second term of the A.P

= First term of the A.P + Common difference

= x+3

Now,if we compare the value of the 2nd term of A.P that we have calculated and the value of the 2nd term of the A.P that is given in the question,we will get the following mathematical equation;

x+3 = 4

x = 4-3

x = 1

Hence,the first term of the given A.P is 1