Advertisements
Advertisements
प्रश्न
Find the sum of all integers between 84 and 719, which are multiples of 5.
Advertisements
उत्तर
The integers between 84 and 719, which are multiples of 5 are:
85, 90...715
Here, we have:
\[a = 85\]
\[d = 5\]
\[ a_n = 715\]
\[ \Rightarrow 85 + (n - 1)5 = 715\]
\[ \Rightarrow 5n - 5 = 630\]
\[ \Rightarrow n = 127\]
\[ S_n = \frac{n}{2}\left[ 2a + (n - 1)d \right]\]
\[ \Rightarrow S_{127} = \frac{127}{2}\left[ 2 \times 85 + (127 - 1)5 \right]\]
\[ \Rightarrow S_{127} = \frac{127}{2}\left[ 800 \right] = 50800\]
APPEARS IN
संबंधित प्रश्न
If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term
Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
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, ...
Find:
18th term of the A.P.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2},\]
How many terms are there in the A.P. 7, 10, 13, ... 43 ?
The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.
The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.
How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?
\[\text { If } \theta_1 , \theta_2 , \theta_3 , . . . , \theta_n \text { are in AP, whose common difference is d, then show that }\]
\[\sec \theta_1 \sec \theta_2 + \sec \theta_2 \sec \theta_3 + . . . + \sec \theta_{n - 1} \sec \theta_n = \frac{\tan \theta_n - \tan \theta_1}{\sin d} \left[ NCERT \hspace{0.167em} EXEMPLAR \right]\]
The sum of three numbers in A.P. is 12 and the sum of their cubes is 288. Find the numbers.
The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.
Find the sum of the following arithmetic progression :
41, 36, 31, ... to 12 terms
Find the sum of all natural numbers between 1 and 100, which are divisible by 2 or 5.
Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.
How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?
The number of terms of an A.P. is even; the sum of odd terms is 24, of the even terms is 30, and the last term exceeds the first by \[10 \frac{1}{2}\] , find the number of terms and the series.
How many terms of the A.P. −6, \[- \frac{11}{2}\], −5, ... are needed to give the sum −25?
If a, b, c is in A.P., then show that:
a2 (b + c), b2 (c + a), c2 (a + b) are also in A.P.
If a, b, c is in A.P., prove that:
(a − c)2 = 4 (a − b) (b − c)
If x, y, z are in A.P. and A1 is the A.M. of x and y and A2 is the A.M. of y and z, then prove that the A.M. of A1 and A2 is y.
A man saves Rs 32 during the first year. Rs 36 in the second year and in this way he increases his savings by Rs 4 every year. Find in what time his saving will be Rs 200.
A man arranges to pay off a debt of Rs 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid, find the value of the first instalment.
A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much the tractor cost him?
If log 2, log (2x − 1) and log (2x + 3) are in A.P., write the value of x.
If Sn denotes the sum of first n terms of an A.P. < an > such that
The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be
If the sum of n terms of an A.P. is 2 n2 + 5 n, then its nth term 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 in an A.P., Sn = n2p and Sm = m2p, where Sr denotes the sum of r terms of the A.P., then Sp is equal to
The first three of four given numbers are in G.P. and their last three are in A.P. with common difference 6. If first and fourth numbers are equal, then the first number is
A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. What is his total earnings during the first year?
Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.
If the sum of n terms of a sequence is quadratic expression then it always represents an A.P
If the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8th terms is ______.
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 ______.
