PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

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 first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.

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 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?

If the 5th and 12th terms of an A.P. are 30 and 65 respectively, what is the sum of first 20 terms?

How many terms of the A.P. −6, \[- \frac{11}{2}\], −5, ... are needed to give the sum −25?

If S₁ be the sum of (2n + 1) terms of an A.P. and S₂ be the sum of its odd terms, then prove that: S₁ : S₂ = (2n + 1) : (n + 1).

Find an A.P. in which the sum of any number of terms is always three times the squared number of these terms.

If the sum of n terms of an A.P. is nP + \[\frac{1}{2}\] n (n − 1) Q, where P and Q are constants, find the common difference.

The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th 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.

If \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P., prove that:

a (b +c), b (c + a), c (a +b) are in A.P.

If a², b², c² are in A.P., prove that \[\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}\] are in A.P.