If the second and fourth terms of G.p are 8and 32,what is the sum off the first 4 terms
Clearly a=4 and r=2
S4 = 4(2^4-1)/(2-1) = 4*15 = 60
check:
4+8+16+32 = 60
To find the sum of the first 4 terms of a geometric progression (G.P.), you need to have the common ratio (r). In this case, we are given the second and fourth terms, which are 8 and 32, respectively.
Let's denote the first term of the G.P. as a, and the common ratio as r.
From the given information, we can form the following equations:
a * r = 8 (equation 1)
a * r^3 = 32 (equation 2)
To find the values of a and r, we can divide equation 2 by equation 1:
(a * r^3) / (a * r) = 32 / 8
This simplifies to:
r^2 = 4
r = 2 (since r cannot be negative in a G.P.)
Substituting r=2 into equation 1:
a * 2 = 8
a = 4
Now that we have found a and r, we can calculate the sum of the first 4 terms of the G.P. using the formula:
Sum of first n terms = a * (r^n - 1) / (r - 1)
For n = 4, a = 4, and r = 2:
Sum = 4 * (2^4 - 1) / (2 - 1)
= 4 * (16 - 1) / 1
= 4 * 15
= 60
Therefore, the sum of the first 4 terms of the given G.P. is 60.