M L Aggarwal Solutions for Exercise 7: Chapter Test

Show that the list of numbers $9, 12, 15, 18, \dots ...$ form an arithmetic progression. Find its ${16}^{\mathrm{th}}$ term and the $n^{\mathrm{th}}$ term.

Find the $6^{\mathrm{th}}$ term from the end of the arithmetic progression $17, 14, 11, \dots , -40$.

If the $8^{\mathrm{th}}$ term of an arithmetic progression is $31$ and the ${15}^{\mathrm{th}}$ term is $16$ more than its ${11}^{\mathrm{th}}$ term, then find the arithmetic progression.

The ${17}^{\mathrm{th}}$ term of an arithmetic progression is $5$ more than twice its $8^{\mathrm{th}}$ term. If the ${11}^{\mathrm{th}}$ term of the arithmetic progression is $43$, then find the $n^{\mathrm{th}}$ term.

The ${19}^{\mathrm{th}}$ term of an arithmetic progression is equal to three times its $6^{\mathrm{th}}$ term. If its $9^{\mathrm{th}}$ term is $19$, find the arithmetic progression.

Which term of the arithmetic progression $5, 2, -1, -4, \dots$ is $-55$?

The ${24}^{\mathrm{th}}$ term of an arithmetic progression is twice its ${10}^{\mathrm{th}}$ term. Show that its ${72}^{\mathrm{nd}}$ term is four times its ${15}^{\mathrm{th}}$ term.

How many terms of the geometric progression $3, \frac{3}{2}, \frac{3}{4}, \dots ...$ are needed to give the sum $\frac{3069}{512}$?