Find 12^2+13^2+14^2+15^2+ +20^2

Question

Find $12^2+13^2+14^2+15^2+\ldots \ldots+20^2$

✓

Answer

$\begin{aligned} & 12^2+13^2+14^2+15^2+\ldots \ldots+20^2 \\ & =\left(1^2+2^2+3^2+4^2+\ldots \ldots .+202\right)-\left(1^2+2^2+3^2+4^2+\ldots \ldots+11^2\right) \\ & =\sum_{r=1}^{20} r^2-\sum_{r=1}^{11} r^2 \text { } \\ & =\frac{20(20+1)(2 \times 20+1)}{6}-\frac{11(11+1)(2 \times 11+1)}{6} \\ & =\frac{20 \times 21 \times 41}{6}-\frac{11 \times 12 \times 23}{6} \\ & =2870-506 \\ & =2364\end{aligned}$

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 "Solve the Following Question.(2 Marks)" from Sequences and Series (p-1)→Sequences and Series (p-1) — all question types→Maths (commerce) STD 11 Commerce / Arts question papers→Maharashtra Board STD 11 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

Solve the inequations: $2|x+3|>1$

→

The letters of the word LOGARTHM are arranged at random. Find the probability that: begins with $O$ and ends with $T$

→

Find the X-intercept of the line x + 2y – 1 = 0.

→

Thirty pairs of values of two variables X and Y are given below. Form a bivariate frequency table. Also find marginal frequency distributions of X and Y.

X	110	88	91	115	97	85	85	91	120	95
Y	500	800	870	599	625	650	905	700	850	824
X	82	105	99	90	108	124	90	90	111	89
Y	970	609	990	735	600	735	729	840	999	780
X	112	100	87	92	91	82	96	120	121	122
Y	638	850	630	720	695	923	555	810	805	526

→

Differentiate the following w.r.t. x. : $\sqrt{x}\left(x^2+1\right)^2$

→

A tree increases annually by $\frac{1}{8}$ of its height. By how much will it increase after $2 \frac{1}{2}$ years. If its length today is $8 \mathrm{~m}$ ?

→

Mr. Manish purchased a motorcycle at ₹ 70,000/-. After some years he sold his motorcycle at its exact depreciated value of it that is $₹ 51,030 /-$. The rate of depreciation was taken as $10 \%$. Find out how many years he sold his motorcycle.

→

Without expanding determinants, prove that

(ii) $\left|\begin{array}{lll}1 & y z & y+z \\ 1 & z x & z+x \\ 1 & x y & x+y\end{array}\right|=\left|\begin{array}{lll}1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2\end{array}\right|$

→

A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that
(i) first is white and second is black?
(ii) one is white and the other is black?

→

Grace Fashion Boutique purchased a sewing machine at $₹ 25,000 /-$. After 3 years machine was sold at depreciated value of $₹ 18,225 /-$. Find the rate of depreciation.

→

X	110	88	91	115	97	85	85	91	120	95
Y	500	800	870	599	625	650	905	700	850	824
X	82	105	99	90	108	124	90	90	111	89
Y	970	609	990	735	600	735	729	840	999	780
X	112	100	87	92	91	82	96	120	121	122
Y	638	850	630	720	695	923	555	810	805	526

X	110	88	91	115	97	85	85	91	120	95
Y	500	800	870	599	625	650	905	700	850	824
X	82	105	99	90	108	124	90	90	111	89
Y	970	609	990	735	600	735	729	840	999	780
X	112	100	87	92	91	82	96	120	121	122
Y	638	850	630	720	695	923	555	810	805	526

Sequences and Series (p-1) — Maths (commerce) STD 11 Commerce / Arts — Question

Answer

Need a full question paper?

Explore more

Similar questions

X	110	88	91	115	97	85	85	91	120	95
Y	500	800	870	599	625	650	905	700	850	824
X	82	105	99	90	108	124	90	90	111	89
Y	970	609	990	735	600	735	729	840	999	780
X	112	100	87	92	91	82	96	120	121	122
Y	638	850	630	720	695	923	555	810	805	526