Question

The 4th and the 9th term of ap are 12 and 27 respectively then find
the values of a and d ​

Answer 1

EXPLANATION.

• GIVEN

4th term of an Ap = 12

9th term of an Ap = 27

Therefore,

TO FIND VALUE OF A AND B.

a4 = a + 3d = 12 ..... (1)

a9 = a + 8d = 27 .....(2)

we get,

-5d = - 15

d = 3

put the value of d in equation (1)

we get,

a + 3(3) = 12

a + 9 = 12

a = 3

Hence,

value of a = 3 and d = 3

Answer 2

Let a and d be a first term and common difference,

T4 = 12

a+(4-1)d= 12

a+3d= 12 (1)

T9 = 27

a+(9-1)d= 27

a+8d = 27 (2)

on subtracting (2) from (1), we get

a + 8d - a - 3d =27 - 12

5d =15

d = 15/5

d = 3

putting the value of d in (1),we get

a+3×3 = 12

a+9 = 12

a =12- 9

a =3

Hence the value of a and d is 3