Question 6

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

Answer

The two-digit numbers, which when divided by 4, yield 1 as remainder, are

13, 17, … 97.

This series forms an A.P. with first term 13 and common difference 4.

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

It is known that the *n*th term of an A.P. is given by, *a**n* = *a* + (*n* –1) *d*

∴97 = 13 + (*n* –1) (4)

⇒ 4 (*n* –1) = 84

⇒ *n* – 1 = 21

⇒ *n* = 22

Sum of *n* terms of an A.P. is given by,

Thus, the required sum is 1210.

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

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

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

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

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

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

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Given a G.P. with

*a*= 729 and 7th term 64, determine S_{7}. - Q:-
Find the sum of all numbers between 200 and 400 which are divisible by 7.

- Q:- Find the sum to n terms of the A.P., whose kth term is 5k + 1.
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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:-
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 first five terms of the sequences whose nth term is \begin{align} a_n = \frac {n}{n+1}\end{align}
- Q:-
Describe the sample space for the indicated experiment: A coin is tossed and a die is thrown.

- 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:-
How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

Siddhant Saxena
2019-09-19 19:39:28

Thanks

Shivangi Mishra
2019-09-14 11:43:16

kindly try to change the background theme.

Yashraj
2019-09-06 22:21:24

Excellent

Sr
2019-07-20 16:40:28

Excellent

Preetam
2016-10-14 01:28:02

Thanks

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