The sum to infinity of a G.P is 60,if the first term is 12, find the nth term.?
The formula for the sum to infinity of a geometric progression (G.P) is given by:
S = a / (1 - r),
where S is the sum to infinity, a is the first term, and r is the common ratio.
In this case, we are given that S = 60 and a = 12. Plugging these values into the formula, we get:
60 = 12 / (1 - r)
Multiplying both sides by (1 - r), we have:
60(1 - r) = 12
60 - 60r = 12
Rearranging the equation, we have:
60r = 48
Dividing both sides by 60, we find:
r = 48/60 = 4/5
Now, we can use the formula for the nth term of a geometric progression:
An = a * r^(n-1),
where An is the nth term, a is the first term, r is the common ratio, and n is the term number.
Plugging in the values a = 12, r = 4/5, and solving for An, we get:
An = 12 * (4/5)^(n-1)
Therefore, the nth term of the G.P is 12 * (4/5)^(n-1).