Embibe Experts Solutions for Chapter: Sequence and Series, Exercise 1: NDA & NA EE 2019 Paper 1 Mathematics

If $p^2, q^2$ and $r^2$ (where $p, q, r>0$) are in $GP,$ then which of the following is/are correct?

1. $p, q$ and $r$ in $GP\mathit{.}$

2. $\ln p, \ln q$ and $\ln r$ are in $AP\mathit{.}$

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Let $a, b, c$ be in $AP$ and $k\ne 0$ be a real number. Which of the following are correct?

1. $ka, kb, kc$ are in $AP$

2. $k-a, k-b, k-c$ are in $AP$

3. $\frac{a}{k}, \frac{b}{k}, \frac{c}{k}$ are in $AP$

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How many two-digit numbers are divisible by $4?$

Let $S_n$ be the sum of the first $n$ terms of an $\mathrm{AP}.$ If $S_{2n}=3n+14n^2,$ then what is the common difference?

If $3^{\mathrm{rd}}, 8^{\mathrm{th}}$ and ${13}^{\mathrm{th}}$ terms of a $\mathrm{GP}$ are $p, q$ and $r$ respectively, then which one of the following is correct?

The numbers $1,5$ and $25$ can be three terms (not necessarily consecutive)of

The sum of $(p+q) th$ and $(p-q) th$ terms of an AP is equal to

What is the fourth term of an $\mathrm{AP}$ of $n$ terms whose sum is $n(n+1) ?$