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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
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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.

This problem has been solved

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