Embibe Experts Solutions for Chapter: Sequences and Series, Exercise 1: Exercise 1

$(5+9+13+17+\dots \text{ up to }23\text{ terms })=?$.

$(0.7+0.71+0.72+\dots \text{ up to }100\text{ terms })=?$.

Which of the following is a sequence?

Let $S_n$ denote the sum of $n$ terms of an$\mathrm{A}.\mathrm{P}.$ whose first term is $a$. If the common difference$d$$=S_n-k S_{n-1}+S_{n-2}$, then find the value of $k$

The first and last term of an$\mathrm{A}. \mathrm{P}.$ are $a$ and $l$ respectively. If $S$is the sum of all the terms of the $\mathrm{A}.\mathrm{P}.$ and the common difference is given by $\frac{l^2-a^2}{k-(l+a)},$ then $k=$

If, $S_1$ is the sum of an arithmetic progression of $n$ odd number of terms and $S_2$ the sum of the terms of the series in odd places, then$\frac{S_1}{S_2}=$

The ${17}^{\mathrm{th}}$ term of the G.P $2,\sqrt{8},4,\sqrt{32},\dots$ is 

$(1+2+3+\dots +80)=?$