This online tool can help you find nth term and the sum of the first n terms of an arithmetic progression. Also, this calculator can be used to solve much more complicated problems. For example, the calculator can find the common difference (d) if a5 = 19 and S7 = 105. The main advantage of this calculator is that it will generate all the work with detailed explanation.
An arithmetic progression is a list of numbers in which the difference between any two successive members is a constant.
Example 1: The sequence of numbers 2, 5, 7, 10, 13,... is arithmetic because the difference between any two consecutive numbers is equal to 3.
Example 2: The sequence 2, 3, 5, 8,... is not arithmetic because the difference between terms is not constant.
Example 3: In the previous sequence, 2, 5, 7, 10, 13,... we have a1 = 2, d = 3, a3= 7, S4 = 24.
Example 4: Find the 7-th element of an arithmetic sequence with d = 3 and a1 = 5.
an = a1 + (n-1)d
a7 = 5 + (7-1)3
a7 = 5 + 6·3
a7 = 5 + 18
a7 = 23
Example 5: Find the sum of first 10 elements of a sequence { 5, 9, 13, 17, 21,...}.
In this example we have a1 = 5, d = 4, and n = 10 since we want to sum up the first n terms.
Sn = n/2[2a1+(n+1)d]
a10 = 10/2[2*5+(10+1)4]
a10 = 5[10+11*4]
a10 = 5[10+44]
a10 = 5[54]
a10 = 108
1. Sum of an arithmetic progression - formula derivation