1+3+5^ 2 +7+9^ 2 + upto 40 terms is equal to - Vidyadip

MCQ

$1+3+5^{2}+7+9^{2}+\ldots$ upto 40 terms is equal to

A
43890
✓
41880
C
33980
D
40870

✓

Answer

Correct option: B.

41880

(B) 41880
$\left(1^{2}+5^{2}+9^{2}+\ldots \ldots\right.$ upto 20 terms$)+(3+7+11+\ldots$upto 20 terms)
$=\sum_{\mathrm{r}=1}^{20}(4 \mathrm{r}-3)^{2}+\sum_{\mathrm{r}=1}^{20}(4 \mathrm{r}-1)$
$=\sum_{r=1}^{20}(4 r-3)^{2}+(4 r-1)$
$=4 \sum_{\mathrm{r}=1}^{20}\left(4 \mathrm{r}^{2}-5 \mathrm{r}+2\right)$
$=16 \sum_{\mathrm{r}=1}^{20} \mathrm{r}^{2}-20 \sum_{\mathrm{r}=1}^{20} \mathrm{r}+8 \sum_{\mathrm{r}=1}^{20} 1=41880$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "SECTION - A [MATHS - MCQ]" from JEE Main 4-April-2025 Paper - Shift 1→JEE Main 4-April-2025 Paper - Shift 1 — all question types→JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $f:( - 1,1) \to B$, be a function defined by $f(x) = {\tan ^{ - 1}}\frac{{2x}}{{1 - {x^2}}},$ then $f$ is both one- one and onto when $B$ is the interval

$\mathop {\lim }\limits_{x \to 0} \,x^2(1+2+3+...+[\frac{1}{|x|}])$ is equal to

(where [.] denotes greatest integer function)

Suppose $a_{1}, a_{2}, \ldots, a_{ n }, \ldots$ be an arithmetic progression of natural numbers. If the ratio of the sum of the first five terms of the sum of first nine terms of the progression is $5: 17$ and $110< a_{15} < 120$ , then the sum of the first ten terms of the progression is equal to -

If $(1 - i)x + (1 + i)y = 1 - 3i,$ then $(x,y) = $

The probability of hitting a target by three marksmen are $\frac{1}{2},\,\frac{1}{3}$ and $\frac{1}{4}$ respectively. The probability that one and only one of them will hit the target when they fire simultaneously, is

Two cards are drawn without replacement from a well-shuffled pack. Find the probability that one of them is an ace of heart

If the straight line $x\cos \alpha + y\sin \alpha = p$ be a tangent to the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$, then

Let $f(x) = {(x + 1)^2} - 1,\;\;(x \ge - 1)$. Then the set $S = \{ x:f(x) = {f^{ - 1}}(x)\} $ is

The number of non-zero integral solutions of the equation $|1 - i{|^x} = {2^x}$ is

If $x = \sin t\cos 2t$ and $y = \cos t\sin 2t$, then at $t = {\pi \over 4},$ the value of ${{dy} \over {dx}}$ is equal to