Commerce (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

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.

If < a_n > is an A.P. such that \[\frac{a_4}{a_7} = \frac{2}{3}, \text { find }\frac{a_6}{a_8}\].

\[\text { If } \theta_1 , \theta_2 , \theta_3 , . . . , \theta_n \text { are in AP, whose common difference is d, then show that }\]

\[\sec \theta_1 \sec \theta_2 + \sec \theta_2 \sec \theta_3 + . . . + \sec \theta_{n - 1} \sec \theta_n = \frac{\tan \theta_n - \tan \theta_1}{\sin d} \left[ NCERT \hspace{0.167em} EXEMPLAR \right]\]

Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.

Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.

The sum of three numbers in A.P. is 12 and the sum of their cubes is 288. Find the numbers.

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 :

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 the following arithmetic progression :

3, 9/2, 6, 15/2, ... to 25 terms

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 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.

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 the following serie:

(a − b)² + (a² + b²) + (a + b)² + ... + [(a + b)² + 6ab]