If the first term of a geometric progression is 5 and the common ratio is 3, wha

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Question: If the first term of a geometric progression is 5 and the common ratio is 3, what is the 3rd term?

Options:

Correct Answer: 135

Solution:

The nth term of a geometric progression is given by a_n = a * r^(n-1). Here, a = 5, r = 3, and n = 3. So, a_3 = 5 * 3^(3-1) = 5 * 3^2 = 5 * 9 = 45.

If the first term of a geometric progression is 5 and the common ratio is 3, what is the 3rd term?

If the first term of a geometric progression is 5 and the common ratio is 3, what is the 3rd term?

Step 1: Identify the first term (a) of the geometric progression, which is given as 5.
Step 2: Identify the common ratio (r) of the geometric progression, which is given as 3.
Step 3: Identify the term number (n) we want to find, which is the 3rd term, so n = 3.
Step 4: Use the formula for the nth term of a geometric progression: a_n = a * r^(n-1).
Step 5: Substitute the values into the formula: a_3 = 5 * 3^(3-1).
Step 6: Calculate the exponent: 3 - 1 = 2, so we have a_3 = 5 * 3^2.
Step 7: Calculate 3^2, which is 9, so now we have a_3 = 5 * 9.
Step 8: Finally, multiply 5 by 9 to get the 3rd term: a_3 = 45.

Geometric Progression – 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.
Nth Term Formula – The formula for finding the nth term of a geometric progression, given by a_n = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.