Advertisements
Advertisements
प्रश्न
Sum of all two digit numbers which when divided by 4 yield unity as remainder is
विकल्प
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:
\[S_{22} = \frac{22}{2}\left\{ 2 \times 13 + \left( 22 - 1 \right)4 \right\}\]
\[ = 11\left\{ 26 + 84 \right\}\]
\[ = 1210\]
APPEARS IN
संबंधित प्रश्न
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.
If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term
The ratio of the sums of m and n terms of an A.P. is m2: n2. Show that the ratio of mth and nthterm is (2m – 1): (2n – 1)
The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
A sequence is defined by an = n3 − 6n2 + 11n − 6, n ϵ N. Show that the first three terms of the sequence are zero and all other terms are positive.
The Fibonacci sequence is defined by a1 = 1 = a2, an = an − 1 + an − 2 for n > 2
Find `(""^an +1)/(""^an")` for n = 1, 2, 3, 4, 5.
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2}, 7\sqrt{2}, . . .\]
Which term of the A.P. 3, 8, 13, ... is 248?
If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.
Find the 12th term from the following arithmetic progression:
3, 8, 13, ..., 253
How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?
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 the following arithmetic progression :
a + b, a − b, a − 3b, ... to 22 terms
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 first n natural numbers.
Find the sum of all natural numbers between 1 and 100, which are divisible by 2 or 5.
Find the sum of all integers between 84 and 719, which are multiples of 5.
Find the sum of the series:
3 + 5 + 7 + 6 + 9 + 12 + 9 + 13 + 17 + ... to 3n terms.
Solve:
1 + 4 + 7 + 10 + ... + x = 590.
Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th 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.
If \[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P., prove that:
\[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P.
If a, b, c is in A.P., prove that:
a3 + c3 + 6abc = 8b3.
Show that x2 + xy + y2, z2 + zx + x2 and y2 + yz + z2 are consecutive terms of an A.P., if x, y and z are in A.P.
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 manufacturer of radio sets produced 600 units in the third year and 700 units in the seventh year. Assuming that the product increases uniformly by a fixed number every year, find (i) the production in the first year (ii) the total product in 7 years and (iii) the product in the 10th year.
If the sum of n terms of an AP is 2n2 + 3n, then write its nth term.
Write the sum of first n odd natural numbers.
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
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 the sum of p terms of an A.P. is q and the sum of q terms is p, show that the sum of p + q terms is – (p + q). Also, find the sum of first p – q terms (p > q).
The sum of terms equidistant from the beginning and end in an A.P. is equal to ______.
The sum of n terms of an AP is 3n2 + 5n. The number of term which equals 164 is ______.
