The sum of 3rd and 4th terms of GP is 108 ,The sum of 4th and 6th term of the same GP is 324 ,find common ratio

Complete Question

The sum of 3rd and 4th terms of GP is 108 ,The sum of 4th and 5th term of the same GP is 324 ,find common ratio

3

Step-by-step explanation:

The formula for Number of term of a GP = ar^n-1

The sum of 3rd and 4th terms of GP is 108

ar² + ar³ = 108... Equation 1

ar²(1+ r) = 108 Equation 1

The sum of 4th and 5th term of the same GP is 324 ,

ar³ + ar⁴= 324... Equation 2

ar³ (1 + r) = 324 Equation 2

find common ratio

ar²(1+ r) = 108 Equation 1

ar³ (1 + r) = 324 Equation 2

Solving for r

ar²(1+ r)/ar³ (1 + r) = 108/324

1/r = 1/3

r = 3

Hence, Common ratio = 3

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54.864 meters

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