In a GP, if the first term is 7 and the common ratio is 1/2, what is the 6th ter

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Question: In a GP, if the first term is 7 and the common ratio is 1/2, what is the 6th term?

Options:

Correct Answer: 0.4375

Solution:

The 6th term is given by 7 * (1/2)^(6-1) = 7 * (1/32) = 0.4375.

In a GP, if the first term is 7 and the common ratio is 1/2, what is the 6th term?

In a GP, if the first term is 7 and the common ratio is 1/2, what is the 6th term?

Step 1: Identify the first term of the GP, which is 7.
Step 2: Identify the common ratio of the GP, which is 1/2.
Step 3: Use the formula for the nth term of a GP: a_n = a * r^(n-1), where a is the first term, r is the common ratio, and n is the term number.
Step 4: Substitute the values into the formula for the 6th term: a_6 = 7 * (1/2)^(6-1).
Step 5: Calculate the exponent: 6 - 1 = 5, so we have a_6 = 7 * (1/2)^5.
Step 6: Calculate (1/2)^5, which is 1/32.
Step 7: Multiply 7 by 1/32: 7 * (1/32) = 7/32.
Step 8: Convert 7/32 to a decimal: 7 divided by 32 equals 0.4375.

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.