if the 10th term of a G.P.is 9 and 4th term is 4, then its 7th term isa)6b)36c)4 9d)9 4Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Answer

The terms of a G.P. are of form a, ar, ar², ar³ ,.... ar⁹ = 9
So, r⁹ = 9 a .....(1)
ar³ = 4 .....(2)
Cubing both sides of (2), we get,
a³r⁹ = 64
putting value of r⁹ in this, we get,

Answer

Given Information:
- 10th term of the G.P. is 9
- 4th term of the G.P. is 4

Formula:
- The nth term of a geometric progression (G.P.) is given by: $a_n = a_1 imes r^{n-1}$

Finding the Common Ratio (r):
- Let the 4th term be $ar^3 = 4$, where a is the first term and r is the common ratio.
- Let the 10th term be $ar^9 = 9$.

Solving for 'r':
- Divide the equation for the 10th term by the equation for the 4th term.
- $\frac{ar^9}{ar^3} = \frac{9}{4}$
- $r^6 = \frac{9}{4}$
- $r = (\frac{9}{4})^{1/6}$

Calculating the 7th term:
- Substitute the value of r back into the equation for the G.P.
- $a_7 = a_1 imes r^{6}$
- $a_7 = a_1 imes (\frac{9}{4})^{1/6}$

Conclusion:
- The 7th term of the G.P. is $a_1 imes (\frac{9}{4})^{1/6}$
- The correct answer is option 'A': 6

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