“The Key Responsibility Of Leadership Is To Think About The Future. No One Else Can Do It For You.”

NCERT EXERCISE 9.3 |

**Question 26.** Insert two numbers between 3 and 81 so that the resulting sequence is G.P.

**Question 27.** Find the value of *n* so that \( \frac{a^{n+1}+b^{n+1}}{a^n+b^n}\) may be the geometric mean between *a* and *b*.

**Question 28.** The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio \( (3+2\sqrt{2}):(3-2\sqrt{2})\).

**Question 29.** If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are \(A pm \sqrt{(A+G)(A-G)}\).

**Question 30.** The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2^{nd} hour, 4^{th} hour and *n*^{th} hour?

**Question 31.** What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?

**Question 32.** If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.