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.
$n$ and $S_n$, if $a=5, d=3$ and $a_n=50$.

✓

Answer

Here, we have an A.P. whose $n ^{\text {th }}$ term ( $a _{ n }$ ), first term $(a)$ and common difference $( d )$ are given, We need to find the number of terms $( n )$ and the sum of first n terms ( $S _{ n }$ ).
Here,
First term (a) $=25$
Last term $\left(a_n\right)=50$
Common difference $( d )=3$
So here we will find the value of $n$ using the formula, an $=a+(n-1) d$
So, substituting the values in the above mentioned formula
$50=5+(n-1) 3$
$50=5+3 n-3$
$50=2+3 n$
$3 n=50-2$
Furhter simplifying for $n$,
$3 n=48$
$n=\frac{48}{3}$
$n=16$
Now, here we can find the sum of the n terms of the given A.P., using the formula,
$S_n=\left(\frac{n}{2}\right)(a+1)$
Where, $a=$ the first term
I = the last term
So, for the givne A.P, on substituting the values in the formula for the sum of n terms of an A.P., we get,
$S_{16}=\left(\frac{16}{2}\right)[5+50]$
$=8(55)$
$=440$
Therefore, for the given A.P. $n=16$ and $S_n=440$

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 "4 Marks Questions" from Arithmetic Progressions→Arithmetic Progressions — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

If the median of the following frequency distribution is 28.5 find the missing frequencies:

Class interval	0-10	10-20	20-30	30-40	40-50	50-60	Total
Frequency	5	$f_1$	20	15	$f_2$	5	60

In the figure $\square ABCD$ is a cyclic quadrilateral. If $m($arc $ABC) = 230^\circ.$ then find $\angle ABC ,\angle CDA ,\angle CBE$

Two dice are rolled, write the sample space ‘S’ and number of sample points
n(S). Also write events and number of sample points in the event according to the
given condition.
(i) Sum of the digits on upper face is a prime number.
(ii) Sum of the digits on the upper face is multiple of 5.
(iii) Sum of the digits on the upper face is 25.
(iv) Digit on the upper face of the first die is less than the digit on the second die.

Four cows are tethered at the four comers of a square field of side 50m such that each can graze the maximum unshared area. What area will be left ungrazed? $[\text{Tale }\pi=3.14]$

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 minutes respectively. In 30 hours, how many times do they toll together?

In $\triangle\text{ABC},$ D and E are the mid-points of AB and AC respectively. Find the ratio of the areas of $\triangle\text{ADE}$ and $\triangle\text{ABC.}$

Evaluate the following:
If $\sin(\text{A}+\text{B})=\sin\text{A}\cos\text{B}+\cos\text{A}\sin\text{B}$ and $\cos(\text{A}-\text{B})=\cos\text{A}\cos\text{B}+\sin\text{A}\sin\text{B},$ Find the values of:

$\sin75^\circ$
$\cos15^\circ.$

In the given figure, MN || BC and AM : MB = 1 : 2
Find $\frac{\text{area}(\triangle\text{AMN})}{\text{area}(\triangle\text{ABC})}.$

Prove analytically that the line segment joining the middle points of two sides of a triangle is equal to half of the third side.

Solve the following quadratic equations by factorization:
$a^2x^2 - 3abx + 2b^2 = 0$