15. The third and fifth terms of G.P are 3 and 27 respectively. Find the eighth term
Answers
Answer:
The n th term of a GP is a.r^(n - 1).
Therefore, the 3rd term is a.r^2 and the 5th term is a.r^4 respectively.
Given that:
a.r^2 = 2 and a.r^4 = 0.5
Dividing the 5th term by the 3rd term:
a.r^4/a.r^2 = 0.5/2
When simplified:
r^2 = 0.25
Therefore:
r = 0.5 or half
Substituting the value of r in a.r^2 = 2:
a.0.5^2 = 2
0.25a = 2
a = 2/0.25
a = 8
Now the sum of a GP is :
Sum = a. (1 - r^n)/1 - r
In your question a = 8, r = 0.5 and n = 5 (because you have requested the first 5 terms)
Therefore:
Sum = 8 x (1 - 0.5^5)/(1 - 0.5)
Sum = 8 x (1 - 0.03125)/0.5
Sum = 8 x 0.96875/0.5
Answer: 15.5
PS: You may just add 8 + 4 + 2 + 1 + 0.5. Which is 15.5.
Learn it using the formula way for higher values of n.
PLEASE NOTE: If the value of r is greater than 1, then the sum formula is:
Sum = a. (r^n - 1)/r - 1