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?
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