English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

The 9^th term of an A.P. is equal to 6 times its second term. If its 5^th term is 22, find the A.P.

If the seventh term of an A.P. is  \[\frac{1}{9}\] and its ninth term is \[\frac{1}{7}\] , find its (63)^rd term.

The sum of 5^th and 9^th terms of an A.P. is 30. If its 25^th term is three times its 8^th term, find the A.P.

Find the sum of the first 15 terms of each of the following sequences having nth term as  x_n = 6 − n .

If the sum of a certain number of terms starting from first term of an A.P. is 25, 22, 19, ..., is 116. Find the last term.

Find the sum of all 2 - digit natural numbers divisible by 4.

Find the sum  (−5) + (−8)+ (−11) + ... + (−230) .

Find the sum:  1 + 3 + 5 + 7 + ... + 199 .

Find the sum \[7 + 10\frac{1}{2} + 14 + . . . + 84\]

If the equation \[\left( 1 + m^2 \right) x^2 + 2 mcx + \left( c^2 - a^2 \right) = 0\] has equal roots, prove that c² = a²(1 + m²).

Find the sum of n terms of the series \[\left( 4 - \frac{1}{n} \right) + \left( 4 - \frac{2}{n} \right) + \left( 4 - \frac{3}{n} \right) + . . . . . . . . . .\]

In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.

In an A.P., the first term is 22, nth term is −11 and the sum to first n terms is 66. Find n and d, the common difference

​The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find its common difference. 

The sum of first 9 terms of an A.P. is 162. The ratio of its 6^th term to its 13^th term is 1 : 2. Find the first and 15^th term of the A.P.

The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28^th term of this A.P.

The sum of first seven terms of an A.P. is 182. If its 4^th and the 17^th terms are in the ratio 1 : 5, find the A.P.