Advertisements
Advertisements
Question
Sum of all two digit numbers which when divided by 4 yield unity as remainder is
Options
1200
1210
1250
none of these.
Advertisements
Solution
1210
The given series is 13, 17, 21....97.
\[a_1 = 13, a_2 = 17, a_n = 97\]
\[d = a_2 - a_1 = 7 - 3 = 4\]
\[a_n = 97\]
\[ \Rightarrow a + \left( n - 1 \right)d = 97\]
\[ \Rightarrow 13 + \left( n - 1 \right)4 = 97\]
\[ \Rightarrow n = 22\]
Sum of the above series:
\[S_{22} = \frac{22}{2}\left\{ 2 \times 13 + \left( 22 - 1 \right)4 \right\}\]
\[ = 11\left\{ 26 + 84 \right\}\]
\[ = 1210\]
APPEARS IN
RELATED QUESTIONS
If the sum of n terms of an A.P. is (pn + qn2), where p and q are constants, find the common difference.
If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
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 = 1 = a2, an = an − 1 + an − 2, n > 2
Find:
10th term of the A.P. 1, 4, 7, 10, ...
Find:
18th term of the A.P.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2},\]
The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.
Find the 12th term from the following arithmetic progression:
3, 8, 13, ..., 253
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.
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.
\[\text { If } \theta_1 , \theta_2 , \theta_3 , . . . , \theta_n \text { are in AP, whose common difference is d, then show that }\]
\[\sec \theta_1 \sec \theta_2 + \sec \theta_2 \sec \theta_3 + . . . + \sec \theta_{n - 1} \sec \theta_n = \frac{\tan \theta_n - \tan \theta_1}{\sin d} \left[ NCERT \hspace{0.167em} EXEMPLAR \right]\]
The sum of three 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 :
41, 36, 31, ... to 12 terms
Find the sum of the following arithmetic progression :
(x − y)2, (x2 + y2), (x + y)2, ... to n 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.
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
Find the sum of all even integers between 101 and 999.
The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.
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 a2, b2, c2 are in A.P., prove that \[\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}\] are in A.P.
If a, b, c is in A.P., then show that:
b + c − a, c + a − b, a + b − c are in A.P.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
In a potato race 20 potatoes are placed in a line at intervals of 4 meters with the first potato 24 metres from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?
A man saved ₹66000 in 20 years. In each succeeding year after the first year he saved ₹200 more than what he saved in the previous year. How much did he save in the first year?
If log 2, log (2x − 1) and log (2x + 3) are in A.P., write the value of x.
Write the value of n for which n th terms of the A.P.s 3, 10, 17, ... and 63, 65, 67, .... are equal.
If m th term of an A.P. is n and nth term is m, then write its pth term.
If the sums of n terms of two AP.'s are in the ratio (3n + 2) : (2n + 3), then find the ratio of their 12th terms.
If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be
If a1, a2, a3, .... an are in A.P. with common difference d, then the sum of the series sin d [sec a1 sec a2 + sec a2 sec a3 + .... + sec an − 1 sec an], 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 \[\frac{S_1}{S_2}\] =
Mark the correct alternative in the following question:
If in an A.P., the pth term is q and (p + q)th term is zero, then the qth term is
Mark the correct alternative in the following question:
The 10th common term between the A.P.s 3, 7, 11, 15, ... and 1, 6, 11, 16, ... is
Write the quadratic equation the arithmetic and geometric means of whose roots are Aand G respectively.
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 ______.
If b2, a2, c2 are in A.P., then `1/(a + b), 1/(b + c), 1/(c + a)` will be in ______
