Arithmetic progressions hard

Arithmetic Progressions Quiz (Hard)

1. Find the sum of the first 50 terms of the arithmetic progression: 2, 12, 22, 32, ...

a) 6000 b) 6500 c) 7000 d) 7500

2. Find the sum of all positive integers less than 1000 which are divisible by 7.

a) 71071 b) 71571 c) 72071 d) 72571

3. In an arithmetic progression, the first term is 5 and the sum of the first n terms is 410. Find the common difference.

a) 10 b) 12 c) 14 d) 16

4. The first term of an arithmetic progression is 3 and the sum of the first 20 terms is 690. Find the common difference.

a) 32 b) 34 c) 36 d) 38

5. Find the sum of all positive integers less than 1000 which are multiples of 4 and 6.

a) 79192 b) 79292 c) 79392 d) 79492

6. Find the sum of all positive integers less than 1000 which are multiples of 5 or 7.

a) 63007 b) 63507 c) 64007 d) 64507

7. The sum of the first n terms of an arithmetic progression is given by the formula:

a) n(n + 1)/2 b) n(2n + 1) c) n(n - 1)/2 d) n(2n - 1)

8. The nth term of an arithmetic progression with first term a and common difference d is given by:

a) a + (n - 1)d b) a + (n + 1)d c) a + nd d) a + 2d

9. The sum of the first 30 terms of the arithmetic progression: 2, 9, 16, 23, ... is:

a) 660 b) 690 c) 720 d) 750

10. The 12th term of an arithmetic progression is 50 and the common difference is 5. What is the first term?

a) 5 b) 10 c) 15 d) 20