Question

The 9th term of a GP is 16 times more than its 5th term. If its 7th term is 96, then find the first term.
please explain​

Answer 1

9th term of GP = ar⁸

5th term.of GP = ar⁴

7th term of GP = ar⁶

[ nth term of a GP = ar^n-1 ]

as per the given data,

ar⁸ = 16*ar⁴____1 and ar⁶ = 96______2

ar⁸/ar⁴ = 16

=> r⁴ = 16

=> r = ± 2

from 2, ar⁶ = 96

putting value of r above, a*2⁶ = 96

=> a*64 = 96

=> a = 96/64

=> a = 3/2

now we know r = ± 2 and a = 3/2

first term.of an GP = a

=> first term = 3/2

in a GP, the sequence goes on like

=> a, ar, ar², ar³, ar⁴ _ _ _ ar^n-1

Answer 2

Answer:

Step-by-step explanation:

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