Answer 1

Here, let us take the first term of the A.P. as a and the common difference of the A.P as d

Now, as we know,

`a_n = a + (n -1 )d`

So for the 7th term (n = 7)

`a_7 = a + (7 - 1)d`

32 = a + 6d .......(1)

Also for 12^th term (n = 13

`a_13 = a + (13 - 1)d`

62 = a + 12d ......(2)

Now on substracting (2) from (1) we get

62 - 32 = (a + 12d) - (a + 6d)

30 = a + 12d - a - 6d

30 = 6d

`d = 30/6`

d = 5

Substiting the value of d in (1) we get

32 = a + 6(5)

32 = a + 30

a = 32 - 30

a = 2

So, the first term is 2 and the common difference is 5.

There the A.P is 2, 7, 12, 27, ....