Tamil Nadu Board Solutions for Chapter: Numbers And Sequences, Exercise 29: Exercise 2.7

Write the first three terms of the G.P. whose first term and the common ratio are given below.

$a=6, r=3$

Write the first three terms of the G.P. whose first term and the common ratio are given below.

$a=\sqrt{2}, r=\sqrt{2}$

Write the first three terms of the G.P. whose first term and the common ratio are given below.

$a=1000, r=\frac{2}{5}$

If $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in A.P. then show that $3^a, 3^b, 3^c$ are in G.P.

In a G.P. the product of three consecutive terms is $27$ and the sum of the product of two terms taken at a time is $\frac{57}{2}$. Find the three terms.

A man joined a company as Assistant Manager. The company gave him a starting salary of $₹60,000$ and agreed to increase his salary $5\%$ annually. If his salary after $5$ years in nearest whole of a rupee $\left(₹\right)$ is $₹k$, then find the value of $k$.

Sivamani is attending an interview for a job and the company gave two offers to him.

Offer $A:₹ 20,000$ to start with followed by a guaranteed annual increase of $6\%$ for the first $5$ years.

Offer $B: ₹ 22,000$ to start with followed by a guaranteed annual increase of $3\%$ for the first $5$ years.

What is his salary in the $4^{\text{th }}$ year with respect to the offers $A$ and $B$?

If $a, b, c$ are three consecutive terms of an A.P. and $x, y, z$ are three consecutive terms of a G.P. then prove that $x^{b-c}\times y^{c-a}\times z^{a-b}=1$