Let there be an A.P. with first term ' a ', common difference ' d… - Vidyadip

Question

Let there be an A.P. with first term ' $a$ ', common difference ' $d$ '. If $a_n$ denotes in $n^{\text {th }}$ term and $S_n$ the sum of first $n$ terms, find. $S _{22}$, if $d =22$ and $a _{22}=149$

✓

Answer

Given $d = 22, a_{22} = 149, n = 22$
We know that
$a_n = a + (n - 1)d$
$149 = a + (22 - 1)22$
$149 = a + 462$
$a = -313$
Now, Sum is given by
$\text{S}_\text{n}=\frac{\text{n}}{2}[2\text{a}(\text{n}-1)\text{d}]$
Where; a = first term for the given A.P.
d = common difference of the given A.P.
n = number of terms
So, using the formula for n = 22, we get
$\text{S}_{22}=\frac{22}{2}\{2\times(-313)+(22-1)\times22)\}$
$\text{S}_{22}=11\{-626+462\}$
$\text{S}_{22}=-1804$
Hence, the sum of 22 terms is -$1804$.

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 "3 Marks Question" from Arithmetic Progressions→Arithmetic Progressions — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

ABC is a triangle in which $\angle\text{A}=90^\circ,\ \text{AN}\perp\text{BC}$ BC = 12cm and AC = 5cm. Find the ratio of the area of $\triangle\text{ANC}$ and $\triangle\text{ABC}.$

The cost of digging a well after every metre of digging, when it costs ₹ $150$ for the first metre and rises by ₹ $50$ for each subsequent metre. Is this situation make an arithmetic progression and why?

Is this $\sqrt 2 ,\sqrt 8 ,\sqrt {18} ,\sqrt {32} ,...$ an AP? If it forms an AP, find the common difference d and write three more terms.

Find the coordinate of the point equidistant from three given points A(5, 3), B(5, -5) and C(1, -5).

Prove that the surface area of a sphere is equal to the curved surface area of the circumscribed cylinder.

Prove that $7 \sqrt { 5 }$ is irrational.

Find the common difference and write the next four terms of the following arithmetic progressions:
$0, -3, -6, -9, .....$

Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2, -1), (1, 0), (4, 3) and (1, 2) meet.

Find the sum of first n odd natural numbers.

Solve the following quadratic equation:$\text{2x}^2-\text{x}+\frac{1}{8}=0$