NCERT Solutions · Class 10 Mathematics Arithmetic Progressions

Which term of the AP : $\displaystyle 121,117,113, \ldots$, is its first negative term? [Hint : Find $\displaystyle n$ for $\displaystyle a_{n}<0$ ]

The sum of the third and the seventh terms of an AP is $\displaystyle 6$ and their product is 8. Find the sum of first sixteen terms of the AP.

A ladder has rungs $\displaystyle 25$ cm apart. (see Fig. $\displaystyle 5.7$). The rungs decrease uniformly in length from $\displaystyle 45$ cm at the bottom to $\displaystyle 25$ cm at the top. If the top and the bottom rungs are $\displaystyle 2 \frac{1}{2} \mathrm{~m}$ apart, what is the length of the wood required for the rungs? [Hint : Number of rungs $\displaystyle =\frac{250}{25}+1$ ]

The houses of a row are numbered consecutively from $\displaystyle 1$ to $\displaystyle 49$ . Show that there is a value of $\displaystyle x$ such that the sum of the numbers of the houses preceding the house numbered $\displaystyle x$ is equal to the sum of the numbers of the houses following it. Find this value of $\displaystyle x$. [Hint : $\displaystyle \mathrm{S}_{x-1}=\mathrm{S}_{49}-\mathrm{S}_{x}$ ]

A small terrace at a football ground comprises of $\displaystyle 15$ steps each of which is $\displaystyle 50$ m long and built of solid concrete. Each step has a rise of $\displaystyle \frac{1}{4} \mathrm{~m}$ and a tread of $\displaystyle \frac{1}{2} \mathrm{~m}$. (see Fig. $\displaystyle 5.8$). Calculate the total volume of concrete required to build the terrace. [Hint : Volume of concrete required to build the first step $\displaystyle =\frac{1}{4} \times \frac{1}{2} \times 50 \mathrm{~m}^{3}$ ] \footnotetext{ * These exercises are not from the examination point of view. }