In a GP, if the first term is 10 and the common ratio is 0.5, what is the 6th te

₹0.0

Question: In a GP, if the first term is 10 and the common ratio is 0.5, what is the 6th term?

Options:

Correct Answer: 0.625

Solution:

The 6th term is given by 10 * (0.5)^(6-1) = 10 * (0.5)^5 = 10 * 0.03125 = 0.3125.

In a GP, if the first term is 10 and the common ratio is 0.5, what is the 6th term?

In a GP, if the first term is 10 and the common ratio is 0.5, what is the 6th term?

Step 1: Identify the first term of the GP, which is given as 10.
Step 2: Identify the common ratio of the GP, which is given as 0.5.
Step 3: To find the 6th term, use the formula for the nth term of a GP: a_n = a_1 * (r)^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.
Step 4: Substitute the values into the formula: a_6 = 10 * (0.5)^(6-1).
Step 5: Calculate the exponent: 6 - 1 = 5, so we have a_6 = 10 * (0.5)^5.
Step 6: Calculate (0.5)^5, which equals 0.03125.
Step 7: Multiply 10 by 0.03125 to find the 6th term: 10 * 0.03125 = 0.3125.

Geometric Progression (GP) – A sequence where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
Formula for nth term of GP – The nth term of a geometric progression can be calculated using the formula: a_n = a * r^(n-1), where 'a' is the first term, 'r' is the common ratio, and 'n' is the term number.