1. Which of the following sequences is an arithmetic progression?
Answer:
Explanation:
The difference between consecutive terms is constant. (3-1=2, 7-3=4, 11-7=4)
2. The 5th term of the AP: 3, 6, 9, 12,… is:
Answer:
Explanation:
Using the formula, a_n = a + (n-1)d, where a is the first term and d is the difference, a_5 = 3 + (5-1)3 = 15.
3. If the first term is 5 and the common difference is 3, the 7th term will be:
Answer:
Explanation:
a_7 = 5 + (7-1)3 = 26.
4. The sum of the first 10 terms of the AP: 2, 4, 6,… is:
Answer:
Explanation:
Using the formula, S_n = n/2(2a + (n-1)d), S_10 = 10/2(2*2 + (10-1)2) = 110.
5. In the AP: 5, 9, 13,… the 50th term is:
Answer:
Explanation:
Using the formula, a_n = a + (n-1)d, a_50 = 5 + (50-1)4 = 197.
6. The difference between consecutive terms in the AP: 7, 10, 13,… is:
Answer:
Explanation:
The difference is 10 – 7 = 3.
7. How many terms of the AP: 4, 7, 10,… must be taken to get a sum of 280?
Answer:
Explanation:
Using the formula for the sum of AP, S_n = n/2(2a + (n-1)d), equate S_n to 280 and solve for n.
8. The 3rd term of an AP is 12 and the 8th term is 27. What is the 10th term?
Answer:
Explanation:
The common difference d = (27-12)/5 = 3. So, the 10th term = 27 + (2 x 3) = 33.
9. If the first and last terms of an AP are 5 and 85 respectively and there are 10 terms in total, what is the common difference?
Answer:
Explanation:
Using the formula a_n = a + (n-1)d, 85 = 5 + (10-1)d. Solving gives d=9.
10. If the nth term of an AP is 2n+1, what is the 1st term?
Answer:
Explanation:
Substituting n=1 in 2n+1 gives 3.
11. The sum of the first n terms of an AP is 3n^2 + 2n. What is the sum of the first two terms?
Answer:
Explanation:
Substituting n=2, we get 3(2^2) + 2(2) = 10.
12. In an AP, if a_3 = 15 and a_8 = 30, what is the common difference?
Answer:
Explanation:
d = (30-15)/5 = 3.
13. The 4th term of an AP is 10. If the common difference is 3, what is the 1st term?
Answer:
Explanation:
a_4 = a + 3d = 10, and d = 3. Solving gives a=1.
14. If the 7th term of an AP is 1/3 and the 10th term is 1/2, what is the common difference?
Answer:
Explanation:
The difference between the terms is (1/2 – 1/3) = 1/6, which is spread over 3 terms. Hence, d = (1/6)/3 = 1/18.
15. The nth term of an AP is given by a_n = 4n – 3. What is the common difference?
Answer:
Explanation:
The nth term is 4n-3 and (n+1)th term is 4(n+1) – 3. The difference between them gives the common difference which is 4.