Enter the first term, common difference, and N-th to calculate the value of the N-th term and the sum of the arithmetic sequence.
An arithmetic sequence is a series of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the common difference. For example, the sequence of even numbers 2, 4, 6, 8, 10 is an arithmetic sequence with a common difference of 2.
The N-th term of an arithmetic sequence can be expressed with the formula:
\( a_n = a_1 + (n - 1) \cdot d \)
Where:
The sum of the first N terms of an arithmetic sequence can be calculated using the following formula:
To calculate based on the first term, last term, and the number of terms:
\( S_n = \frac{n}{2} \cdot (a_1 + a_n) \)
Or,
To calculate based on the first term, common difference, and the number of terms:
\( S_n = \frac{n}{2} \cdot (2a_1 + (n - 1) \cdot d) \)
Where \( S_n \) is the sum of the first N terms.
Solution:
Calculate the 5th term:
\( a_5 = 20 + (5 - 1) \cdot 4 = 20 + 16 = 36 \)
Calculate the sum:
\( S_5 = \frac{5}{2} \cdot (20 + 36) = \frac{5}{2} \cdot 56 = 140 \)
Solution:
Calculate the 4th term:
\( a_4 = 5 + (4 - 1) \cdot (-1) = 5 - 3 = 2 \)
Calculate the sum:
\( S_4 = \frac{4}{2} \cdot (5 + 2) = 2 \cdot 7 = 14 \)
Solution:
Calculate the 8th term:
\( a_8 = 50 + (8 - 1) \cdot 6 = 50 + 42 = 92 \)
Calculate the sum:
\( S_8 = \frac{8}{2} \cdot (50 + 92) = 4 \cdot 142 = 568 \)