In a GP, if the first term is 2 and the common ratio is -2, what is the 4th term

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Question: In a GP, if the first term is 2 and the common ratio is -2, what is the 4th term?

Options:

Correct Answer: -8

Solution:

The 4th term is given by 2 * (-2)^(4-1) = 2 * (-8) = -16.

In a GP, if the first term is 2 and the common ratio is -2, what is the 4th term?

In a GP, if the first term is 2 and the common ratio is -2, what is the 4th term?

Step 1: Identify the first term of the GP, which is given as 2.
Step 2: Identify the common ratio of the GP, which is given as -2.
Step 3: To find the 4th term, use the formula for the nth term of a GP: 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 = 2, r = -2, and n = 4.
Step 5: Calculate the exponent: n - 1 = 4 - 1 = 3.
Step 6: Now calculate the 4th term: 2 * (-2)^3.
Step 7: Calculate (-2)^3, which is -2 * -2 * -2 = -8.
Step 8: Now multiply: 2 * (-8) = -16.
Step 9: The 4th term of the GP is -16.

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.