Arithmetic progression - practice problems

An arithmetic progression (AP) is a sequence of numbers where the difference between any two consecutive terms is a constant value. This constant difference is called the common difference.

Formula for n-th member is:

a_{n} = a_{1} + (n - 1) \cdot d

Sum of n AP members:

s_{n} = n \cdot \frac{a _{1} + a _{n}}{2}

Number of problems found: 406

The sum 53
The sum ofthree numbers of a GP series is 35 and their product is 1000. Find the numbers.
A person 2
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.
The median 3
The median of the following observations arranged in ascending order is 64: 27, 31, 46, 52, x, x + 4, 71, 79, 85, 90 Find the value of x.
Common difference
What is the common difference of an AP (arithmetic progression) in which a₁₈ – a₁₄ = 32
Doubling every day
If you start with 1 euro on day 1 and double your money daily, how many days before you get at least 1 million?
Binary series
The 4th term of a G.P. is 16 and the 7th term is 128 . Find the first term and common ratio of the series.
Quadrilateral angles in AP
The four angles of a quadrilateral form an arithmetic progression. If the common difference is 15°, then find all the angles.
Consecutive odd nums
Sum of four consecutive odd numbers is 40. Find the numbers.
The common difference 2
Find the common difference of an arithmetic progression (AP), whose first term is 5 and sum of its first 4 terms is half the sum of the next four terms.
Split 207
Split number 207 into three parts such that these are in the arithmetic progression (AP) and the product of two smaller parts is 4623.
Descent GP
Determine the 18th term of the GP whose 5th term is 1 and common ratio is 2/3.
Negative term
Which term of the AP 24,21,18,15,.....is the first negative term?
The common difference
Find the common difference of an arithmetic progression (AP), whose 1st term is 5 and the sum of its 1st 4 terms is half the sum of the next four terms.
What will
What will be the average of the numbers from 1 to 51?
The average 13
The average of 6 consecutive odd numbers is 64. Find the greatest number.
The sum 47
The sum of 3 numbers in an arithmetic progression (AP) is 15. If 1,4,19 are to be added to the above numbers respectively, it formed a geometric progression (GP). Find the numbers.
Series - double GP
In the following series, which number will replace the question mark? 4, 32, 16, 128, 64,?
The 5th
The 5th, 8th and 11th terms of a GP are a, b, c respectively. Show that a, b, c are in GP.
The sum 46
The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
The angles 5
The angles of a triangle are in arithmetic progression (AP). The greatest angle is twice the least. Find all the angles.

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