In a geometric progression, if the first term is 4 and the common ratio is 1/2,

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Question: In a geometric progression, if the first term is 4 and the common ratio is 1/2, what is the 6th term?

Options:

Correct Answer: 0.25

Solution:

The 6th term is given by a * r^(n-1) = 4 * (1/2)^(6-1) = 4 * (1/32) = 4/32 = 0.125.

In a geometric progression, if the first term is 4 and the common ratio is 1/2, what is the 6th term?

In a geometric progression, if the first term is 4 and the common ratio is 1/2, what is the 6th term?

Step 1: Identify the first term (a) of the geometric progression, which is given as 4.
Step 2: Identify the common ratio (r) of the geometric progression, which is given as 1/2.
Step 3: Identify the term number (n) we want to find, which is the 6th term, so n = 6.
Step 4: Use the formula for the nth term of a geometric progression: a * r^(n-1).
Step 5: Substitute the values into the formula: 4 * (1/2)^(6-1).
Step 6: Calculate the exponent: (6-1) = 5, so we have 4 * (1/2)^5.
Step 7: Calculate (1/2)^5, which is 1/32.
Step 8: Now multiply: 4 * (1/32) = 4/32.
Step 9: Simplify 4/32 to get 0.125.

Geometric Progression – A sequence of numbers 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 – The nth term of a geometric progression can be calculated using the formula a * r^(n-1), where 'a' is the first term, 'r' is the common ratio, and 'n' is the term number.