Question 4

Find the sum of all numbers between 200 and 400 which are divisible by 7.

Answer

The numbers lying between 200 and 400, which are divisible by 7, are

203, 210, 217, … 399

∴First term, *a* = 203

Last term, *l* = 399

Common difference, *d* = 7

Let the number of terms of the A.P. be *n*.

∴ *a*_{n} = 399 = *a* + (*n* –1) *d*

⇒ 399 = 203 + (*n* –1) 7

⇒ 7 (*n* –1) = 196

⇒ *n* –1 = 28

⇒ *n* = 29

Thus, the required sum is 8729.

- Q:-
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

- Q:-
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

- Q:-
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

- Q:- Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
- Q:-
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

- Q:-
How many terms of G.P. 3, 3

^{2}, 3^{3}, … are needed to give the sum 120? - Q:- Write the following sets in roster form:

(i) A = {x: x is an integer and - 3 < x < 7}.

(ii) B = {x: x is a natural number less than 6}.

(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}

(iv) D = {x: x is a prime number which is divisor of 60}.

(v) E = The set of all letters in the word TRIGONOMETRY.

(vi) F = The set of all letters in the word BETTER. - Q:-
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

- Q:-
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

- Q:-
The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7th term.

- Q:- Write the following sets in roster form:

(i) A = {x: x is an integer and - 3 < x < 7}.

(ii) B = {x: x is a natural number less than 6}.

(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}

(iv) D = {x: x is a prime number which is divisor of 60}.

(v) E = The set of all letters in the word TRIGONOMETRY.

(vi) F = The set of all letters in the word BETTER. - Q:-
Find the sum to

*n*terms of the series whose*n*th term is given by*n*(*n*+ 1) (*n*+ 4). - Q:-
Show that the sum of (

*m*+*n*)th and (*m*–*n*)th terms of an A.P. is equal to twice the*m**t*h term. - Q:- Write the following sets in the set-builder form:

(i) (3, 6, 9, 12)

(ii) {2, 4, 8, 16, 32}

(iii) {5, 25, 125, 625}

(iv) {2, 4, 6 upto infinity}

(v) {1, 4, 9, upto 100} - Q:-
Find the sum to

*n*terms in the geometric progression 1,-a, a^{2},-a^{3}, ... (if a ≠ -1) - Q:-
A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

- Q:-
The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to

*n*terms of the G.P. - Q:-
Find the sum to

*n*terms of the series 3 × 8 + 6 × 11 + 9 × 14 +… - Q:-
Find a G.P. for which sum of the first two terms is –4 and the fifth term is 4 times the third term.

- Q:-
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

Harsh
2019-08-22 21:32:16

Good

saranya
2019-02-18 18:52:33

ummma thank you

Neelam
2019-01-07 13:03:24

But how I know that first no. Is 203

David N Maikundu
2018-11-09 16:44:45

thank you great elucidation

David N Maikundu
2018-11-09 16:32:27

wonderfull explanation

Shilpa
2018-09-20 12:53:07

Thank you for your help

DHARMAPADA KARUA
2018-06-03 11:06:42

Good solution.

Puru
2017-10-10 21:25:27

Thanks for the explanation

shethra krishna
2016-11-16 07:34:16

it was a wonderful explanation

karthik
2016-10-12 14:20:48

Good explanation

- NCERT Chapter