CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Sum of N Terms of an AP

What is the s...

Question

What is the sum of the arithmetic series $1 + 3 + 5 + 7 + 9 + . . . + 99 ?$

A

1500

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

2500

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

C

3500

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

4500

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $2500$
$a_{n} = a + (n - 1) d$
$\Rightarrow 99 = 1 + (n - 1) 2$
$\Rightarrow 99 - 1 = 2 n - 2$
$\Rightarrow 98 + 2 = 2 n$
$\Rightarrow 100 = 2 n$
$\Rightarrow n = 50$
$S_{n} = \frac{n}{2} [a_{1} + a_{n}]$
$\Rightarrow S_{n} = \frac{50}{2} [1 + 99]$
$\Rightarrow S_{n} = 25 [100]$
$\Rightarrow S_{n} = 2500$

Suggest Corrections

thumbs-up

0

Similar questions

Q. The following data gives the distribution of total monthly household expenditure of

200

families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.

Expenditure (in Rs.)	Frequency	Expenditure (in Rs.)	Frequency
1000-1500	$24$	3000-3500	$30$
1500-2000	$40$	3500-4000	$22$
2000-2500	$33$	4000-4500	$16$
2500-3000	$28$	4500-5000	$7$

Q. The following data gives the distribution of total monthly household expenditures of

200

families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.

$E x p e n d i t u r e$ (In Rs)	Number of families
$1000 - 1500$	$24$
$1500 - 2000$	$40$
$2000 - 2500$	$33$
$2500 - 3000$	$28$
$3000 - 3500$	$30$
$3500 - 4000$	$22$
$4000 - 4500$	$16$
$4500 - 5000$	$7$

Q. The following table gives the distribution of the life time of

400

Life time: (in hours)	Number of lamps
$1500 - 2000$	$14$
$2000 - 2500$	$56$
$2500 - 3000$	$60$
$3000 - 3500$	$86$
$3500 - 4000$	$74$
$4000 - 4500$	$62$
$4500 - 5000$	$48$

Find the median life.

The weekly salaries of employees in railway department are as follows. Given the mean salaries is $2900$ Rs. and assumed mean is $1250$ .

Salary(Rs)	Number of employees
$1000 - 1500$	$12$
$1500 - 200$	$19$
$2000 - 2500$	$23$
$2500 - 3000$	$24$
$3000 - 3500$	Y
$3500 - 4000$	$16$
$4000 - 4500$	$27$

Q. The following table gives the distribution of the life time of 400 neon lamps:

Life time (in hours)	Number of lamps
$1500 - 2000$ $2000 - 2500$ $2500 - 3000$ $3000 - 3500$ $3500 - 4000$ $4000 - 4500$ $4500 - 5000$	$14$ $56$ $60$ $86$ $74$ $62$ $48$

Find the median life time of a lamp.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Sum of n Terms of an AP

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Sum of N Terms of an AP

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon