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The fourth and seventh terms of geometrical progression are 72 and 576.

Find the first term and the common ratio



User Samwu
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To find the first term and the common ratio of a geometric progression, we can use the formula for the nth term of a geometric progression:

An = A * r^(n-1)

where An is the nth term, A is the first term, r is the common ratio, and n is the term number.

Given that the fourth term (n=4) is 72 and the seventh term (n=7) is 576, we can set up two equations:

72 = A * r^(4-1)

576 = A * r^(7-1)

Let's solve these equations step by step:

Equation 1: 72 = A * r^3

Equation 2: 576 = A * r^6

Now, divide equation 2 by equation 1 to eliminate A:

576/72 = (A * r^6)/(A * r^3)

8 = r^6/r^3

8 = r^(6-3)

8 = r^3

Taking the cube root of both sides, we get:

r = 2

Substituting this value of r into equation 1 to find A:

72 = A * 2^3

72 = A * 8

Dividing both sides by 8, we find:

A = 9

Therefore, the first term (A) of the geometric progression is 9, and the common ratio (r) is 2.

User Chris Duncan
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