If first term of a G.P. is 20 and common ratio is 4. Find the 5th term.Options102405120256040960
Question
If first term of a G.P. is 20 and common ratio is 4. Find the 5th term.
Options:
- 1024
- 40512
- 2560
- 40
- 960
Solution
The formula to find the nth term of a geometric progression (G.P.) is:
a_n = a * r^(n-1)
where:
- a_n is the nth term
- a is the first term
- r is the common ratio
- n is the term number
Given in the problem:
- a (first term) = 20
- r (common ratio) = 4
- n (term number) = 5
Substitute these values into the formula:
a_5 = 20 * 4^(5-1)
Simplify the exponent:
a_5 = 20 * 4^4
Calculate 4^4:
a_5 = 20 * 256
Finally, multiply 20 by 256 to get the 5th term:
a_5 = 5120
So, the 5th term of the geometric progression is 5120.
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