Advertisements
Advertisements
प्रश्न
How many numbers of two digit are divisible by 3?
Advertisements
उत्तर
The two digit numbers that are divisible by 3 are:
12, 15, 18...96, 99
This is an A.P. whose first term is 12 and the common difference is 3.
\[\text { We have }: \]
\[ a_n = 99\]
\[ \Rightarrow 12 + (n - 1)3 = 99\]
\[ \Rightarrow (n - 1)3 = 87\]
\[ \Rightarrow (n - 1) = 29\]
\[ \Rightarrow n = 30\]
Thus, there are 30 such terms.
संबंधित प्रश्न
Find the sum of odd integers from 1 to 2001.
Sum of the first p, q and r terms of an A.P. are a, b and c, respectively.
Prove that `a/p (q - r) + b/q (r- p) + c/r (p - q) = 0`
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
Let < an > be a sequence. Write the first five term in the following:
a1 = a2 = 2, an = an − 1 − 1, n > 2
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
3, −1, −5, −9 ...
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
9, 7, 5, 3, ...
The nth term of a sequence is given by an = 2n + 7. Show that it is an A.P. Also, find its 7th term.
Find:
nth term of the A.P. 13, 8, 3, −2, ...
Which term of the A.P. 4, 9, 14, ... is 254?
Is 302 a term of the A.P. 3, 8, 13, ...?
How many terms are there in the A.P.\[- 1, - \frac{5}{6}, -\frac{2}{3}, - \frac{1}{2}, . . . , \frac{10}{3}?\]
If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.
The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms.
Find the sum of the following arithmetic progression :
\[\frac{x - y}{x + y}, \frac{3x - 2y}{x + y}, \frac{5x - 3y}{x + y}\], ... to n terms.
Find the sum of the following serie:
101 + 99 + 97 + ... + 47
Find the sum of first n natural numbers.
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 17. Find the progression.
If \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P., prove that:
\[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P.
If a, b, c is in A.P., prove that:
(a − c)2 = 4 (a − b) (b − c)
A man saved Rs 16500 in ten years. In each year after the first he saved Rs 100 more than he did in the receding year. How much did he save in the first year?
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalments of Rs 1000 plus 10% interest on the unpaid amount. How much the scooter will cost him.
A man accepts a position with an initial salary of ₹5200 per month. It is understood that he will receive an automatic increase of ₹320 in the very next month and each month thereafter.
(i) Find his salary for the tenth month.
(ii) What is his total earnings during the first year?
If \[\frac{3 + 5 + 7 + . . . + \text { upto n terms }}{5 + 8 + 11 + . . . . \text { upto 10 terms }}\] 7, then find the value of n.
If m th term of an A.P. is n and nth term is m, then write its pth term.
In n A.M.'s are introduced between 3 and 17 such that the ratio of the last mean to the first mean is 3 : 1, then the value of n is
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
If the sum of p terms of an A.P. is q and the sum of q terms is p, show that the sum of p + q terms is – (p + q). Also, find the sum of first p – q terms (p > q).
Let Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn then S3n: Sn is equal to ______.
If n AM's are inserted between 1 and 31 and ratio of 7th and (n – 1)th A.M. is 5:9, then n equals ______.
The sum of n terms of an AP is 3n2 + 5n. The number of term which equals 164 is ______.
If a1, a2, a3, .......... are an A.P. such that a1 + a5 + a10 + a15 + a20 + a24 = 225, then a1 + a2 + a3 + ...... + a23 + a24 is equal to ______.
If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is ______.
The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is ______.
For an A.P. with first term \(a\) and common difference \(d\), the common difference is computed as:
Which of the following is an example of a Constant A.P.?
