M L Aggarwal Solutions for Chapter: Sequences and Series, Exercise 3: EXERCISE 10.3

If $2+5+8+\dots +x=155$, then find $x$.

If the sum of first $7$ terms of an $\mathrm{A}.\mathrm{P}.$ is $10$ and that of next $7$ terms is $17$ find its ${28}^{th}$ term.

A spiral is made of successive semicircles, with centres alternately at $A$ and $B$, starting with centre at $A$ of radii $0.5\mathrm{cm},1.0\mathrm{cm}$ $1.5\mathrm{cm},\dots$ as shown in the adjoining figure. What is the total length of such a spiral made up of thirteen consecutive semicircles. Take $\pi =\frac{22}{7}$.

A ladder (shown in the figure) has rungs $25\mathrm{cm}$ apart. The rungs decrease uniformly in length from $45\mathrm{cm}$ at the bottom to $25\mathrm{cm}$ 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?

A carpenter was hired to build $192$ window frames. The first day he made five frames and each day, thereafter he made two more frames than he made the day before. How many number of days did it take him to finish the job?

A circle is completely divided into $n$ sectors in such a way that the angles of the sectors are in arithmetic progression. If the smallest of these angles is $8°$ and the largest $72°$, calculate $n$ and the angle in the fourth sector.

An $\mathrm{N}.\mathrm{G}.\mathrm{O}$ wants to invest $₹300000$  in a bond which pays $5\%$ annual interest first year, $6\%$ interest second year, $7\%$ interest third year and so on. The interest received per year is to be utilized for the education of poor people. If the investment is done for $10$ years, find the total interest received by $\mathrm{N}.\mathrm{G}.\mathrm{O}.$ Which value is reflected in the question?

Kumar buys a maruti car for $₹2,40,000$ at a down payment of $₹1,20,000$ and the rest in annual instalments of $₹10,000$ plus $12\%$ interest on the unpaid amount. Eventually what will the car cost him?