Embibe Experts Solutions for Chapter: Numbers and Sequences, Exercise 1: Tamilnadu Board-2018

If $a, b, c$ are in G.P., then $\frac{a-b}{b-c}$ is equal to:

The next term of the series $\sqrt{3}, \sqrt{12}, \sqrt{27}...$ is:

Three numbers are in ratio $2:5:7$. If the first number, the resulting number on subtraction of $7$ form the second number and the third number form an arithmetic sequence, then find the numbers.

ln the  division algorithm of polynomials the divisor is $\left(x+2\right)$, quotient is $\left(x-1\right)$ and the remainder ts $4$. Find the dividend.

Find the three consecutive terms in an A.P. whose sum is $18$ and the sum of their squares is $140$.

The first term of a geometric series is $375$ and the fourth term is $192$. Find the common ratio and the sum of the first $14$ terms.

Find the sum of the series $5^2+7^2+9^2+ ........ +{39}^2$.

The $4^{\mathrm{th}}$ term of a geometric sequence is $\frac{2}{3}$ and its seventh term is $\frac{16}{81}$. Find the geometric sequence.