Question

In an ap the difference between 8th and 4th term is 20 and the 8th term is 1.5 times the 4th term
A. Find the common difference
B. First term

Answer 1

Dear Student

Let the first term be 'a'
And, the common difference be 'd'
The nth term will be: a+(n-1)d
So, the 8th term is a+7d
The 4th term is a+3d

As per the question:
(a+7d)-(a+3d) = 20
Or, 4d = 20
Or, d = 5

Now, (a+7d) = 1.5(a+4d)
Or, a+7d = 1.5a + 6d
Or, 0.5a = d
Or, a = d/0.5
Or, a = 4/0.5 = 8

AnsA. Common difference= 4
AnsB. First term= 8

Regards