Advertisements
Advertisements
प्रश्न
Sum of all two digit numbers which when divided by 4 yield unity as remainder is
पर्याय
1200
1210
1250
none of these.
Advertisements
उत्तर
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:
\[S_{22} = \frac{22}{2}\left\{ 2 \times 13 + \left( 22 - 1 \right)4 \right\}\]
\[ = 11\left\{ 26 + 84 \right\}\]
\[ = 1210\]
संबंधित प्रश्न
Find the sum to n terms of the A.P., whose kth term is 5k + 1.
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.
if `a(1/b + 1/c), b(1/c+1/a), c(1/a+1/b)` are in A.P., prove that a, b, c are in A.P.
A manufacturer reckons that the value of a machine, which costs him Rs 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.
Let < an > be a sequence. Write the first five term in the following:
a1 = 1, an = an − 1 + 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.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2},\]
Which term of the A.P. 84, 80, 76,... is 0?
Which term of the sequence 24, \[23\frac{1}{4,} 22\frac{1}{2,} 21\frac{3}{4}\]....... is the first negative term?
The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.
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.
Find the sum of the following arithmetic progression :
50, 46, 42, ... to 10 terms
Find the sum of the following arithmetic progression :
1, 3, 5, 7, ... to 12 terms
Find the sum of first n odd natural numbers.
Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.
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 sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 17. Find the progression.
The third term of an A.P. is 7 and the seventh term exceeds three times the third term by 2. Find the first term, the common difference and the sum of first 20 terms.
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.
If Sn = n2 p and Sm = m2 p, m ≠ n, in an A.P., prove that Sp = p3.
Find the sum of n terms of the A.P. whose kth terms is 5k + 1.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
Find the sum of odd integers from 1 to 2001.
Find an A.P. in which the sum of any number of terms is always three times the squared number of these terms.
The sums of first n terms of two A.P.'s are in the ratio (7n + 2) : (n + 4). Find the ratio of their 5th terms.
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.
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.
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.
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:
\[\text { If in an A . P } . S_n = n^2 q \text { and } S_m = m^2 q, \text { where } S_r \text{ denotes the sum of r terms of the A . P . , then }S_q \text { equals }\]
The first term of an A.P. is a, the second term is b and the last term is c. Show that the sum of the A.P. is `((b + c - 2a)(c + a))/(2(b - a))`.
If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad
If the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8th terms 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 ______.
