Which term of the G.P. 5, 10, 20, 40, … is 5120 ?

The given sequence is a geometric progression (G.P.) where each term is multiplied by a common ratio to get the next term.

The general formula for the nth term of a G.P. is given by a*r^(n-1), where:

• a is the first term of the sequence,
• r is the common ratio, and
• n is the term number.

In this case, a = 5 (the first term), r = 2 (each term is twice the previous term), and we want to find n such that the nth term is 5120.

So, we set up the equation 5*2^(n-1) = 5120 and solve for n:

1. Divide both sides by 5: 2^(n-1) = 1024
2. Recognize that 1024 is a power of 2: 1024 = 2^10, so 2^(n-1) = 2^10
3. Since the bases are equal, the exponents must be equal: n-1 = 10
4. Solve for n: n = 10 + 1 = 11

So, the 11th term of the geometric progression is 5120.