Welcome Class 11 Maths MCQ – Sequences and Series chapter. Here, we curated a set of 20 multiple-choice questions to test your knowledge of the Sequences and Series in Maths

## 1. The common difference of the arithmetic sequence 2, 5, 8, 11,… is:

### Answer:

### Explanation:

The difference between any two consecutive terms is 3.

## 2. The sum of the first 10 terms of an arithmetic series is 505. What is the 10th term?

### Answer:

### Explanation:

Using the formula for the sum of n terms and given that n=10, we find the 10th term is 55.

## 3. If the nth term of an arithmetic sequence is 4n + 1, what is the 5th term?

### Answer:

### Explanation:

Plug n=5 into the formula to get 4(5) + 1 = 21.

## 4. The common ratio of the geometric sequence 3, 6, 12, 24,… is:

### Answer:

### Explanation:

Each term is twice the previous term.

## 5. The sum of the first three terms of a geometric progression is 13 and their product is 27. The first term is:

### Answer:

### Explanation:

Let the terms be a, ar, and ar^2. Given, a(1 + r + r^2) = 13 and a^3 * r^3 = 27. Solving gives a = 1.

## 6. The sum of the infinite geometric series 1/2 + 1/4 + 1/8 + … is:

### Answer:

### Explanation:

Using the formula for the sum of an infinite GP, S = a/(1-r), where a = 1/2 and r = 1/2.

## 7. The nth term of the sequence 1, 4, 9, 16,… is:

### Answer:

### Explanation:

Each term is the square of its position in the sequence.

## 8. Which of the following sequences is neither arithmetic nor geometric?

### Answer:

### Explanation:

The differences between consecutive terms are not constant, and the ratios are not constant.

## 9. If the sum of the first n terms of a sequence is given by S_n = n^2 + n, then the nth term is:

### Answer:

### Explanation:

The nth term is S_n – S_(n-1). This gives n^2 + n – [(n-1)^2 + (n-1)] = n + 1.

## 10. The sum of the first 6 terms of the series 2 + 5 + 8 + … is:

### Answer:

### Explanation:

Using the formula for the sum of n terms of an AP, we get 91.

## 11. If the 4th term of an AP is 0, which of the following must be true?

### Answer:

### Explanation:

Without additional information, none of the given options can be definitively concluded.

## 12. The sum of n terms of the series 1 + 3 + 5 + … is:

### Answer:

### Explanation:

The given series is of odd numbers, and the sum of the first n odd numbers is n^2.

## 13. The sum of the series 1^2 + 2^2 + 3^2 + … + n^2 is:

### Answer:

### Explanation:

This is the formula for the sum of the squares of the first n natural numbers.

## 14. The sum of the first n terms of the sequence whose nth term is given by a_n = 2n – 1 is:

### Answer:

### Explanation:

The given sequence is of odd numbers, and the sum of the first n odd numbers is n^2.

## 15. In a GP, if the 2nd term is 4 and the 4th term is 64, the 3rd term is:

### Answer:

### Explanation:

In a GP, the ratio remains constant. Hence, the 3rd term would be the square root of (4th term/2nd term) = 16.

## 16. The nth term of the sequence 1, 1/2, 1/3, 1/4,… is:

### Answer:

### Explanation:

Each term is the reciprocal of its position in the sequence.

## 17. The nth term of the sequence 2, 5, 10, 17,… is:

### Answer:

### Explanation:

The nth term is n squared plus n.

## 18. The sum of the infinite geometric series 1 + x + x^2 + x^3 + … where |x|<1 is:

### Answer:

### Explanation:

This is the formula for the sum of an infinite GP with the given condition.

## 19. Which of the following is a harmonic progression?

### Answer:

### Explanation:

A sequence is a harmonic progression if the reciprocals of its terms form an arithmetic progression.

## 20. The sum of the first n terms of an arithmetic progression is given by S_n = 2n^2 + 5n. What is the common difference?

### Answer:

### Explanation:

The nth term a_n = S_n – S_(n-1). By subtracting consecutive terms, the common difference is found to be 4.