Find the sum of the first 60 terms of the arithmetic sequence whose first term is −15 and whose common difference is 7.
a60 = a1 + (59)(7)
a60 = -15 + 413 = 398
S60 = 60 (-15 + 398) / 2
=11490
Why did the arithmetic sequence go to therapy?
Because it had some negative terms and needed to work on its positivity!
But getting back to your question, to find the sum of the first 60 terms of an arithmetic sequence, we can use the formula:
Sn = (n/2)(2a + (n-1)d),
where Sn is the sum of the first n terms, a is the first term, and d is the common difference.
Using this formula, we can substitute the given values:
n = 60,
a = -15,
d = 7.
Sn = (60/2)(2(-15) + (60-1)7)
= (30)(-30 + 413)
= 30(383)
= 11,490.
So, the sum of the first 60 terms of the arithmetic sequence is 11,490.
To find the sum of the first 60 terms of an arithmetic sequence, we can use the formula:
Sn = (n/2)(2a + (n-1)d)
Where:
- Sn is the sum of the first n terms
- a is the first term
- d is the common difference
- n is the number of terms
In this case, a = -15, d = 7, and n = 60:
Sn = (60/2)(2(-15) + (60-1)(7))
= 30(-30 + 59(7))
= 30(-30 + 413)
= 30(383)
= 11,490
The sum of the first 60 terms of the given arithmetic sequence is 11,490.
To find the sum of the first 60 terms of an arithmetic sequence, we can use the formula:
Sn = n/2 * (2a + (n-1)d),
where Sn represents the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.
For the given arithmetic sequence:
a = -15 (first term)
d = 7 (common difference)
n = 60 (number of terms)
Substituting these values into the formula:
S60 = 60/2 * (2(-15) + (60-1)7)
Simplifying further:
S60 = 30 * (-30 + 413)
S60 = 30 * 383
S60 = 11,490
Therefore, the sum of the first 60 terms of the arithmetic sequence is 11,490.