Question -
Answer -
Let the series be 3, A1,A2, A3, …….., An, 17
Given, an/a1 =3/1
We know total terms inAP are n + 2
So, 17 is the (n +2)th term
By using the formula,
An = a+ (n – 1)d
An =17, a = 3
So, 17 = 3 + (n + 2 –1)d
17 = 3 + (n + 1)d
17 – 3 = (n + 1)d
14 = (n + 1)d
d = 14/(n+1)
Now,
An = 3+ 14/(n+1) = (17n + 3) / (n+1)
A1 = 3+ d = (3n+17)/(n+1)
Since,
an/a1 =3/1
(17n + 3)/ (3n+17) =3/1
17n + 3 = 3(3n + 17)
17n + 3 = 9n + 51
17n – 9n = 51 – 3
8n = 48
n = 48/8
= 6
∴ There are 6 terms inthe AP