Hi Anil,
If 10th term of a GP is 9 and 4th term is 4, then find its 7th term
We know that
an = arn – 1
where an = nth term of GP
n is the number of terms
a is the first term
r is the common ratio
10th term
a10 = 9
ar10 – 1 = 9
ar9 = 9
…(1)
4th term
a4 = 4
ar4 – 1 = 4
ar3 = 4
…(2)
Dividing (1) by (2)
(ar^9)/(ar^3 ) = 9/4
r^9/r^3 = 9/4
r^(9-3) = 9/4
r^6 = 9/4
Now,
Taking square root both sides
(r^6 )^(1/2) = (9/4)^(1/2)
r^3 = (3^2/2^2 )^(1/2)
r^3 = (3/2)^(2/2)
r3 = 3/2
From (2)
ar3 = 4
Putting r3 = 3/2 from (2)
a × 3/2 = 4
a = 4 × 2/3
a = 8/3
Now we need to find 7th term,
We use the formula
an = arn – 1
Putting n = 7 , a = 8/3
a7 = 8/3 r^(7-1)
a7 = 8/3 × r^6
Putting r^6 = 9/4 from (3)
a7 = 8/3 × 9/4
a7 = 6
Hence, 7th term is 6
Written on May 2, 2017, 7:28 p.m.