Daily Practice Problems

Class 11 Maths

Sequences and Series

Class 11 Maths

Sequences and Series

**Question 1:**

In an AP, if m^{th} term is n and the n^{th} term is m, where m ≠ n, find the p^{th }term.

**Question 2:**

A man saved Rs. 66000 in 20 years. In each succeeding year after the first year, he saved Rs. 200 more than what he saved in the previous year. How much did he save in the first year?

**Question 3:**

A carpenter was hired to build 192 window frames. The first day he made five frames and each day, thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?

**Question 4:**

If 2x, x + 8, 3x + 1 are in A.P, then what is the value of x?

**Question 5:**

Find the sum of the series (3^{3} – 2^{3}) + (5^{3} – 4^{3}) + (7^{3} – 6^{3}) + … to n terms.

**Question 6:**

If 9 times the 9^{th} term of an A.P. is equal to 13 times the 13^{th} term, then find the 22^{nd} term of the A.P.

**Question 7:**

Write the first five terms of the sequences whose n^{th} term is a_{n} = n *

**Question 8:**

If T_{n} denotes the n^{th} term of the series 2 + 3 + 6 + 11 + 18 + …, then T_{50} is ____.

**Question 9:**

In an A.P. if p^{th} term is 1q and q^{th} term is1p , prove that the sum of first pq terms is , where p ≠ q. where p ≠ q.

**Question 10:**

If x, 2y and 3z are in A.P. where the distinct numbers x, y and z are in G.P., then find the common ratio of the G.P.

**Question 11:**

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

**Question 12:**

Find the sum to n terms of the sequence: 3, 33, 333, 3333, ......

**Question 13:**

In a G.P., the 3^{rd }term is 24 and the 6^{th} term is 192. Find the 10^{th} term.

**Question 14:**

If a, b, c are in GP then log a^{n}, log b^{n}, log c^{n} are in _____.

**Question 15:**

A person has 2 parents, 4 grandparents, 8 great grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own.

**Question 16:**

The sum of n terms of the series + + + …… is _____.

**Question 17:**

The first term of a GP is 1. The sum of the third term and fifth term is 90. The common ratio of GP is ______.

**Question 18:**

Find the value of n so that may be may be the geometric mean between a and b.

**Question 19:**

Find the sum to n terms of the series 3 * 8 + 6 * 11 + 9 * 14 +........

**Question 20:**

Find the sum to n terms of the series whose n^{th} term is n(n + 3).

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