hi please help me
Find the sum of the first 8 terms of the arithmetic sequence 30, 33, 36, 39, 42, 45, . . .
thank you.
To find the sum of the first 8 terms of an arithmetic sequence, you can use the arithmetic series formula. The formula is:
Sn = (n/2)(2a + (n-1)d)
Where:
- Sn is the sum of the first n terms
- a is the first term of the sequence
- d is the common difference between the terms
- n is the number of terms
In this case, we are given the first term (a = 30), and we need to find the sum of the first 8 terms (n = 8). Additionally, we can find the common difference by subtracting the second term from the first term. In this sequence, the second term is 33, so the common difference (d) is 33 - 30 = 3.
Now, let's plug these values into the formula:
Sn = (8/2)(2(30) + (8-1)(3))
= 4(60 + 7(3))
= 4(60 + 21)
= 4(81)
= 324
Therefore, the sum of the first 8 terms of the arithmetic sequence 30, 33, 36, 39, 42, 45, ..., is 324.