The 1st term of a geometric
progression is 2 and the 5th term is 512. Find the common ratio.
Solution
G1=2, G5=512,
n=5
Gn = G1rn-1;
G5 = G1r5-1;
G5 = G1r4;
512 = 2 x r4;
512 = 2r4;
2
2
256 = r4; Finding the
fourth root of 256,
We do prime factorization of 256.
2 |
256 |
2 |
128 |
2 |
64 |
2 |
32 |
2 |
16 |
2 |
8 |
2 |
4 |
2 |
2 |
|
1 |
44 = r4; [equal
powers will cancel out]
4 = r
r = 4
Hence the common ratio is 4.
TRY THIS …………..
The 1st term of a geometric
progression is 3 and the 5th term is 9375. Find the common ratio.