The 4th term of geometric progression is 2/3and the seventh term is 16/81.find the geometric series
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Answer:
9/4, 3/2, 1, 2/3 ....
Step-by-step explanation:
Formula for nth term of GP = Tₙ = arⁿ⁻¹.
T₄ = ar³ = 2/3 --------------- [1]
T₇ = ar⁶ = 16/81 -------------- [2]
Divide [2] by [1]
ar⁶/ar³ = 16/81 / 2/3
r³ = 16/81 * 3/2 = 8/27 = (2/3)³
=> r = 2/3.
Substitute value of r in [1]
ar³ = 2/3
=> a (2/3)³ = 2/3
=> a = 2/3 * 27/8 = 9/4.
Thus the geometric series = 9/4, 3/2, 1, 2/3 ....
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