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.
APPEARS IN
संबंधित प्रश्न
Find the sum of odd integers from 1 to 2001.
If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7th and (m – 1)th numbers is 5:9. Find the value of m.
A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.
A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.
Let < an > be a sequence. Write the first five term in the following:
a1 = 1 = a2, an = an − 1 + an − 2, n > 2
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:
18th term of the A.P.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2},\]
Find:
nth term of the A.P. 13, 8, 3, −2, ...
If the sequence < an > is an A.P., show that am +n +am − n = 2am.
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. 7, 10, 13, ... 43 ?
How many terms are there in the A.P.\[- 1, - \frac{5}{6}, -\frac{2}{3}, - \frac{1}{2}, . . . , \frac{10}{3}?\]
If (m + 1)th term of an A.P. is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.
Find the 12th term from the following arithmetic progression:
1, 4, 7, 10, ..., 88
The first and the last terms of an A.P. are a and l respectively. Show that the sum of nthterm from the beginning and nth term from the end is a + l.
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
Find the sum of the following arithmetic progression :
(x − y)2, (x2 + y2), (x + y)2, ... to n terms
Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.
If the sum of a certain number of terms of the AP 25, 22, 19, ... is 116. Find the last term.
Find the sum of odd integers from 1 to 2001.
If a, b, c is in A.P., prove that:
(a − c)2 = 4 (a − b) (b − c)
A piece of equipment cost a certain factory Rs 600,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?
A carpenter was hired to build 192 window frames. The first day he made five frames and each day thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?
We know that the sum of the interior angles of a triangle is 180°. Show that the sums of the interior angles of polygons with 3, 4, 5, 6, ... sides form an arithmetic progression. Find the sum of the interior angles for a 21 sided polygon.
In a cricket team tournament 16 teams participated. A sum of ₹8000 is to be awarded among themselves as prize money. If the last place team is awarded ₹275 in prize money and the award increases by the same amount for successive finishing places, then how much amount will the first place team receive?
Write the sum of first n odd natural numbers.
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
The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =
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 first, second and last term of an A.P are a, b and 2a respectively, then its sum is
If, S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then \[\frac{S_1}{S_2}\] =
If a, b, c are in G.P. and a1/x = b1/y = c1/z, then xyz are in
The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest. Find the numbers
Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.
The sum of n terms of an AP is 3n2 + 5n. The number of term which equals 164 is ______.
