Question

if the 10 th term of a G. P. is 9 th and 4 th term is4, then what is its7 th term??
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Answer 1

Answer:

Let the first term and common ratio of the given G.P be a and respectively.

T10 = ar9 = 9 ––––––(1)

T4 = ar³ = 4 —————(2)

T10/T4 = ar9/ar³= 9/4

r6 = 9/4

(r³)² = 9/4

r³ = 3/2

from (1) ar9 = 9

a(r³) = 9

Substituting the value of r³ from (iii) we get

a(3/2)³ = 9

a = 9×8/27 = 8/3

T7 = ar6 = 8/3 × 9/4 =6

I hope this is helps you.

Answer 2

Answer:

be the first term of GP with common ratio r.

The nth term, an = arn-1

10th term, ar9 = 9…(i)

4th term, ar3 = 4…(ii)

Multiply (i) and (ii)

ar9ar3 = 36

a2r12 = 36

(ar6)2 = 36

Taking square root

ar6 = 6

So 7th term = ar6 = 6

Hence option (1) is the answer

Step-by-step explanation:

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