# Arithmetic Progression: Solved Examples

Q1. Find the sum of all three digit numbers that leave a remainder of '1' when divided by 3?
A. 897
B. 1,64,850
C. 1,64,749
D. 1,49,700
Q2. What is the sum of all positive integers up to 1000, which are divisible by 5 and are not divisible by 2?
A. 10,050
B. 5050
C. 5000
D. 50,000
Q3. The sum of the 3 numbers in A.P is 21 & the product of the first & third number of the sequence is 45. What are the 3 numbers?
A. 5, 7, and 9
B. 9, 7, and 5
C. 3, 7, and 11
D. Both (A) and (B)
Q4. A piece of equipment costs a certain factory INR 600,000. If it depreciates in value, 15% in the first year, 13.5 % in the next year, 12% in the third year, and so on, what will be its value at the end of the 10 years, all percentages applying to original cost?
A. 2,00,000
B. 1,05,000
C. 4,05,000
D. 6,50,000
5. The sum of third and ninth term of an A.P is 8. Find the sum of the first 11 terms of the progression.
A. 44
B. 22
C. 19
D. None of the above
Q.6. An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
A. 25
B. 64
C. 50
D. 27
Q.7. How many 2-digit positive integers are divisible by 4 or 9?
A. 32
B. 22
C. 30
D. 34
Q8. x, 17, 3x – y2 - 2 and 3x + y2 - 30 are four consecutive terms of an increasing arithmetic sequence. The sum of the 4 numbers is divisible by:
A. 2
B. 3
C. 5
D. 7
Q9. What is the sum of the following series? -64, -66, -68, ..... , -100
A. -1458
B. -1558
C. -1568
D. -1664
Q10. If log 2, log (2x -1) and log (2x + 3) are in A.P, then x is equal to ____
A. 5252
B. log25
C. log32
D. 32