To find the sum of the arithmetic sequence, we first need to identify the first term, the common difference, and the number of terms.
In this sequence:
- The first term (t) is 8.
- The second term is 15, leading to a common difference (d) of 15 – 8 = 7.
- The number of terms (n) is given as 26.
To find the sum (S_n) of the first n terms of an arithmetic sequence, we can use the formula:
S_n = n/2 * (2a + (n – 1)d)
Where:
- S_n is the sum of the first n terms.
- a is the first term.
- d is the common difference.
- n is the number of terms.
Plugging in the values:
- a = 8
- d = 7
- n = 26
Now we can calculate the sum:
S_n = 26/2 * (2 * 8 + (26 – 1) * 7)
S_n = 13 * (16 + 25 * 7)
S_n = 13 * (16 + 175)
S_n = 13 * 191
S_n = 2483
Therefore, the sum of the arithmetic sequence with 26 terms is 2483.