Mahabir Singh Solutions for Chapter: Arithmetic Progressions, Exercise 3: ACHIEVERS SECTION (HOTS)

Which of the following statement is CORRECT?
$a.$ Sum of n terms of the list of the numbers $\sqrt{2},\sqrt{8},\sqrt{18},\sqrt{32},\dots is \frac{n(n+1)}{\sqrt{2}}$

$b.$ The common difference of A.P. given by $a_n=3n+2$ is $3.$

$c.$ The sum of the A.P. $(-5),(-8),(-11),...(-230)is-8930$

If there are $(2n+1)$ terms in A.P. then find the ratio of the sum of odd terms to the sum of even terms.

If $\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$ is the A.M. between $a$ and $b$, then find the value of $n$

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

If the ratio of sum of n terms of two A.P. is $(7n+1):(4n+27),$ then ratio of their $m^{th}$ term is ____

Sum of n odd natural number is ____

If sum if n terms of three A.P. are $S_1,S_2,S_3$ . The first term of each is 1 and common difference are $\mathrm{1,} 2, 3$ respectively, then $\frac{S_1+S_3}{S_2}=\_\_\_\_\_\_\_$