Question

The 8th term of an ap is 5th term the 3rd term while the 7th term is 9 greater than 4 term. What is the 1 term of the ap?

Answer 1

If your question means:

The 8th term of an ap is 5 times the 3rd term while the 7th term is 9 greater than 4 term. What is the 1 term of the ap?

then:

In AP

an = a1 + ( n - 1) d

a1 = first term

d = common diference

a3 = a1 + 2 d

a4 = a1 + 3 d

a7 = a1 + 6 d

a8 = a1 + 7 d

The 8th term of an ap is 5 times the 3rd term means:

a8 = 5 a3

a1 + 7 d = 5 ( a1 + 2 d )

a1 + 7 d = 5 a1 + 10 d

Subtract 5 a1 to both sides.

- 4a1 + 7 d = 10 d

Subtract 7d to both sides.

- 4a1 = 3 d

Multiply both sides by - 1 / 4

a1 = - 3 / 4 d

7th term is 9 greater than 4 term means:

a1 + 6 d = a1 + 3 d + 9

Subtract a1 to both sides.

6 d = 3 d + 9

Subtract 3d to both sides.

3 d = 9

d = 9 / 3

d = 3

a1 = - 3 / 4 d = - 3 • 3 / 4

a1 = - 9 / 4