What is the sum of the arithmetic sequence 4, 11, 18 …, if there are 26 terms?
d = 11-4 = 81-11 = 7
Sn = (n/2)(2a1 + (n-1)d)
S26 = (26/2)(2*4 + 25(7)
To find the sum of an arithmetic sequence, you can use the formula:
Sn = (n/2) * (a + L)
Where Sn is the sum of the sequence, n is the number of terms, a is the first term, and L is the last term.
In this case, the first term, a, is 4 and the last term, L, can be found by using the formula for the nth term of an arithmetic sequence:
Ln = a + (n-1)d
Where Ln is the last term, n is the number of terms, a is the first term, and d is the common difference between terms.
In this case, the common difference, d, can be found by subtracting the first term from the second term:
d = 11 - 4 = 7
Now we can find the last term, L:
L = 4 + (26-1)*7 = 4 + 25*7 = 4 + 175 = 179
Finally, we can calculate the sum of the sequence:
Sn = (26/2) * (4 + 179) = 13 * 183 = 2379
Therefore, the sum of the arithmetic sequence 4, 11, 18 ..., with 26 terms is 2379.