English Medium Class 10 - CBSE Question Bank Solutions

If the sum of first p terms of an AP is 2 (ap²  +  bp), find its common difference.

If the sum of first n terms is  (3n² +  5n), find its common difference.

Find an AP whose 4^th  term is 9 and the sum of its 6^th and 13^th terms is 40. 

Find the sum of the following Aps:

i) 2, 7, 12, 17, ……. to 19 terms . 

Find the sum of  the following Aps:

9, 7, 5, 3 … to 14 terms

Find the sum of first n terms of an AP whose nth term is (5 - 6n). Hence, find the sum of its first 20 terms.

The sum of the first n terms of an AP is (3n²+6n) . Find the nth term and the 15^th term of this AP. 

The sum of the first n terms of an AP is given by  `s_n = ( 3n^2 - n) ` Find its

(i) nth term,
(ii) first term and
(iii) common difference.

The sum of the first n terms of an AP in `((5n^2)/2 + (3n)/2)`.Find its nth term and the 20th term of this AP.

The sum of the first n terms in an AP is `( (3"n"^2)/2 +(5"n")/2)`. Find the n^th term and the 25^th term.

How many terms of the AP 21, 18, 15, … must be added to get the sum 0?

How many terms of the AP 63, 60, 57, 54, ….. must be taken so that their sum is 693? Explain the double answer.

How many terms of the AP `20, 19 1/3 , 18 2/3, ...` must be taken so that their sum is 300? Explain the double answer.

Find the sum of all natural numbers between 200 and 400 which are divisible by 7.

Find the sum of all multiples of 9 lying between 300 and 700.

If the ratio of sum of the first m and n terms of an AP is m² : n², show that the ratio of its  m^th and n^th terms is (2m − 1) : (2n − 1) ?

Find the positive value(s) of k for which quadratic equations x² + kx + 64 = 0 and x² – 8x + k = 0 both will have real roots ?

Find the 25^th term of the AP \[- 5, \frac{- 5}{2}, 0, \frac{5}{2}, . . .\]

The fourth term of an A.P. is 11. The sum of the fifth and seventh terms of the A.P. is 34. Find its common difference.

Solve for x :

x² + 5x − (a² + a − 6) = 0