Advertisements
Advertisements
प्रश्न
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
Advertisements
उत्तर
The two-digit numbers which when divided by 4 yield 1 as remainder are 13, 17....97.
\[\therefore a = 13, d = 4, a_n = 97\]
\[ \therefore a_n = a + (n - 1)d\]
\[ \Rightarrow 97 = 13 + (n - 1)4\]
\[ \Rightarrow 84 = 4n - 4\]
\[ \Rightarrow 88 = 4n\]
\[ \Rightarrow 22 = n . . . \left( 1 \right)\]
\[\text { Also }, S_n = \frac{n}{2}\left[ 2a + (n - 1)d \right]\]
\[ S_{22} = \frac{22}{2}\left[ 2 \times 13 + (22 - 1) \times 4 \right] (\text { From }\left( 1 \right))\]
\[ \Rightarrow S_{22} = 11\left[ 110 \right] = 1210\]
संबंधित प्रश्न
Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio of their 18th terms
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`
If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
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.
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 ...
Find:
10th term of the A.P. 1, 4, 7, 10, ...
Is 68 a term of the A.P. 7, 10, 13, ...?
The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.
How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?
If < an > is an A.P. such that \[\frac{a_4}{a_7} = \frac{2}{3}, \text { find }\frac{a_6}{a_8}\].
Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.
Find the sum of the following serie:
2 + 5 + 8 + ... + 182
Find the sum of the following serie:
101 + 99 + 97 + ... + 47
Find the sum of all integers between 100 and 550, which are divisible by 9.
Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.
If the 5th and 12th terms of an A.P. are 30 and 65 respectively, what is the sum of first 20 terms?
How many terms of the A.P. −6, \[- \frac{11}{2}\], −5, ... are needed to give the sum −25?
In an A.P. the first term is 2 and the sum of the first five terms is one fourth of the next five terms. Show that 20th term is −112.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
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?
Write the common difference of an A.P. the sum of whose first n terms is
Sum of all two digit numbers which when divided by 4 yield unity as remainder 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 =
Mark the correct alternative in the following question:
\[\text { If in an A . P } . S_n = n^2 q \text { and } S_m = m^2 q, \text { where } S_r \text{ denotes the sum of r terms of the A . P . , then }S_q \text { equals }\]
Mark the correct alternative in the following question:
Let Sn denote the sum of first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
Write the quadratic equation the arithmetic and geometric means of whose roots are Aand G respectively.
If a, b, c are in A.P. and x, y, z are in G.P., then the value of xb − c yc − a za − b is
If a, b, c are in G.P. and a1/x = b1/y = c1/z, then xyz are in
The pth term of an A.P. is a and qth term is b. Prove that the sum of its (p + q) terms is `(p + q)/2[a + b + (a - b)/(p - q)]`.
The sum of terms equidistant from the beginning and end in an A.P. is equal to ______.
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 100 times the 100th term of an A.P. with non zero common difference equals the 50 times its 50th term, then the 150th term of this A.P. is ______.
The internal angles of a convex polygon are in A.P. The smallest angle is 120° and the common difference is 5°. The number to sides of the polygon is ______.
For an A.P. with first term \(a\) and common difference \(d\), the common difference is computed as:
