Algebra 2 B Arithmetic series 5 Questions
what is the sum of the finite arithmetic series 26+29+32+35+38+41+44
1.b 245
2.b
3.b
4.c
5.a 26
To find the sum of a finite arithmetic series, you 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 between terms
- n is the number of terms
In this case, a=26, d=3 (we can see that each term is increased by 3 from the previous term), and there are 7 terms. So we can plug these values into the formula:
S_7 = 7/2 * [2(26) + (7-1)(3)]
S_7 = 7/2 * [52 + 18]
S_7 = 7/2 * 70
S_7 = 245
Therefore, the sum of the finite arithmetic series is 245.
A Human is correct!
To find the sum of a finite arithmetic series, you can use the formula:
Sn = (n/2)(2a + (n-1)d)
Where:
Sn = the sum of the series
n = the number of terms
a = the first term
d = the common difference between consecutive terms
In this case, the first term (a) is 26 and the common difference (d) is 3. However, we need to determine the number of terms (n) in the series.
To find the number of terms, we can use the formula:
tn = a + (n-1)d
Where:
n = the number of terms
tn = the nth term of the series
a = the first term
d = the common difference
In this case, we have tn = 44. Substituting the known values into the formula:
44 = 26 + (n-1)3
Now, we solve for n:
44 = 26 + 3n - 3
44 - 26 = 3n - 3
18 = 3n - 3
21 = 3n
n = 7
So, the number of terms (n) in the series is 7.
Now that we know n, we can substitute the values into the sum formula:
Sn = (n/2)(2a + (n-1)d)
Sn = (7/2)(2(26) + (7-1)(3))
Sn = (7/2)(52 + 6 × 3)
Sn = (7/2)(52 + 18)
Sn = (7/2)(70)
Sn = 490/2
Sn = 245
Therefore, the sum of the finite arithmetic series 26+29+32+35+38+41+44 is 245.