The sum of the first 10 terms of the arithmetic sequence 2, 5, 8, 11 is 155.
Understanding Arithmetic Sequences and Series
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the common difference. In the given sequence, 2, 5, 8, 11,..., the common difference is 3 (5-2 = 3, 8-5 = 3, and so on).
An arithmetic series is the sum of the terms of an arithmetic sequence. To find the sum of the first n terms of an arithmetic series, we can use the formula:
Sn = n/2 * [2a + (n-1)d]
Where:
- Sn is the sum of the first n terms.
- n is the number of terms.
- a is the first term.
- d is the common difference.
Calculating the Sum of the First 10 Terms
In this case, we want to find the sum of the first 10 terms (n = 10) of the arithmetic sequence 2, 5, 8, 11,... The first term (a) is 2, and the common difference (d) is 3.
Using the formula:
S10 = 10/2 [2(2) + (10-1)3]
S10 = 5 [4 + (9)3]
S10 = 5 [4 + 27]
S10 = 5 [31]
S10 = 155
Therefore, the sum of the first 10 terms of the arithmetic sequence 2, 5, 8, 11 is 155, as confirmed by the provided reference which states: "Then we can use the formula Sn = 10/2(2(2) + (10-1)3) = 10/2(4 + 27) = 10/2(31) = 155. Therefore, the sum of the first 10 terms of the arithmetic series 2, 5, 8, 11, 14 is 155."
