Find the sum of the following arithmetic progression: (x - y)^2, … - Vidyadip

Question

Find the sum of the following arithmetic progression: $(x - y)^2, (x^2 + y^2), (x + y)^2$ ... to $n$ terms.

✓

Answer

$(x - y)^2, (x^2 + y^2), (x + y)^2$ ... to $n$ terms. $\text{s}_\text{n}=\frac{\text{n}}{2}[2\text{a}+(\text{n}-1)\text{d}]$ $=\frac{\text{n}}{2}\big[2(\text{x}^2+\text{y}^2-2\text{xy})+(\text{x}-1)(-2\text{xy})\big]$ $=\text{n}[(\text{x}-\text{y})^2+(\text{n}-1)\text{xy}]$

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 "(Each question 2 marks)" from Arithmetic Progressions→Arithmetic Progressions — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Describe the following sets in Roster form: {x : x is a two digit number such that the sum of its digits is 8}

Express the (-i)(2i)$\left (- \frac 18 i\right)^3$ in the form of a + bi:

A bag contains one white and one red ball. A ball is drawn from the bag. If the ball drawn is white it is replaced in the bag and again a ball is drawn. Otherwise, a die is tossed. Write the sample space for this experiment.

In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

Convert the following products into factorials: 5.6.7.8.9.10

Let $X=\{1,2,3,4\}$ and $Y=\{1,5,9,11,15,16\}$. Determine which of the following sets are functions from $X$ to $Y: f_1=$ $\{(1,1),(2,11),(3,1),(4,15)\}$

Find the equation of the line which satisfy the given conditions:
Passing through $(2,2 \sqrt{3})$ and inclined with the x-axis at an angle of $75^o$.

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^{\text{x}}-\text{e}^5}{\text{x}-5}$

Find the component statements of the following compound statements and check whether they are true or false. All integers are positive or negative.

Write the contrapositive and converse of the following statements. You cannot comprehend geometry if you do not know how to reason deductively.