If the second term of a geometric progression is 12 and the common ratio is 3, w

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Question: If the second term of a geometric progression is 12 and the common ratio is 3, what is the first term?

Options:

Correct Answer: 4

Solution:

Let the first term be a. The second term is a * r = a * 3 = 12, thus a = 12/3 = 4.

If the second term of a geometric progression is 12 and the common ratio is 3, what is the first term?

If the second term of a geometric progression is 12 and the common ratio is 3, what is the first term?

Step 1: Identify the first term of the geometric progression as 'a'.
Step 2: Understand that the second term can be calculated by multiplying the first term 'a' by the common ratio 'r'.
Step 3: Since the common ratio 'r' is given as 3, write the equation for the second term: second term = a * r = a * 3.
Step 4: We know from the question that the second term is 12, so we can set up the equation: a * 3 = 12.
Step 5: To find 'a', divide both sides of the equation by 3: a = 12 / 3.
Step 6: Calculate the value: a = 4.

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.
Common Ratio – The factor by which we multiply each term to get the next term in a geometric progression.
Solving for Variables – The process of isolating a variable in an equation to find its value.