If the first term of a GP is 7 and the common ratio is 3, what is the 6th term?

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Question: If the first term of a GP is 7 and the common ratio is 3, what is the 6th term?

Options:

Correct Answer: 729

Solution:

The 6th term is given by 7 * 3^(6-1) = 7 * 243 = 1701.

If the first term of a GP is 7 and the common ratio is 3, what is the 6th term?

If the first term of a GP is 7 and the common ratio is 3, what is the 6th term?

Step 1: Identify the first term of the geometric progression (GP), which is given as 7.
Step 2: Identify the common ratio of the GP, which is given as 3.
Step 3: To find the 6th term, 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: a_6 = 7 * 3^(6-1).
Step 5: Calculate the exponent: 6 - 1 = 5, so we have a_6 = 7 * 3^5.
Step 6: Calculate 3^5, which is 3 * 3 * 3 * 3 * 3 = 243.
Step 7: Now multiply 7 by 243: 7 * 243 = 1701.
Step 8: Therefore, the 6th term of the GP is 1701.

Geometric Progression (GP) – 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 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.