Assam Board Solutions for Chapter: Arithmetic Progressions, Exercise 4: Exercise 5.4

Which term of the $\mathrm{A}\mathrm{P}$: $121,\mathrm{}117,\mathrm{}113,\mathrm{}.\mathrm{}.\mathrm{}.,$ is its first negative term?

The sum of the third and the seventh terms of an $\mathrm{}\mathrm{A}\mathrm{P}$ is $\mathrm{}6$ and their product is $\mathrm{}8$. Find the sum of first sixteen terms of the $\mathrm{}\mathrm{A}\mathrm{P}$.

A ladder has rungs $25 \mathrm{cm}$  apart. (See Fig.). The rungs decrease uniformly in length from $45 \mathrm{c}\mathrm{m}$ at the bottom to $25 \mathrm{c}\mathrm{m}$ at the top. If the top and the bottom rungs are $2\frac{1}{2} \mathrm{m}$ apart, what is the length of the wood required for the rungs?

The houses of a row are numbered consecutively from $\mathrm{}1$ to $\mathrm{}49$. Show that there is a value of $\mathrm{}x$ such that the sum of the numbers of the houses preceding the house numbered $\mathrm{}x$ is equal to the sum of the numbers of the houses following it. Find this value of $\mathrm{}x$.

A small terrace at a football ground comprises of $\mathrm{}15$ steps each of which is $50 \mathrm{m}$ long and built of solid concrete.
Each step has a rise of $\frac{1}{4}\mathrm{}\mathrm{m}$ and a tread of $\frac{1}{2}\mathrm{m}$. (see Fig.). Calculate the total volume of concrete required to build the terrace.