Calculate the sum of each of the following arithmetic sequence:
1). 3+8+13+
2). 20+17+14
3). -2-7-2+
4). -3-7-11
5). 2q+6q+10q+
1) The common difference in this arithmetic sequence is 5. To find the sum, we can use the formula:
Sum = (n/2)(first term + last term), where n is the number of terms.
First term = 3
Last term = 13
n = (last term - first term)/common difference + 1 = (13 - 3)/5 + 1 = 11/5 + 1 = 2.2 + 1 = 3.2
Sum = (3.2/2)(3 + 13) = 1.6 * 16 = 25.6
Therefore, the sum of the arithmetic sequence 3+8+13+ is 25.6.
2) The common difference in this arithmetic sequence is -3. To find the sum, we can use the formula:
Sum = (n/2)(first term + last term), where n is the number of terms.
First term = 20
Last term = 14
n = (last term - first term)/common difference + 1 = (14 - 20)/-3 + 1 = -6/-3 + 1 = 2 + 1 = 3
Sum = (3/2)(20 + 14) = 1.5 * 34 = 51
Therefore, the sum of the arithmetic sequence 20+17+14 is 51.
3) The common difference in this arithmetic sequence is -5. To find the sum, we can use the formula:
Sum = (n/2)(first term + last term), where n is the number of terms.
First term = -2
Last term = -2
n = (last term - first term)/common difference + 1 = (-2 - (-2))/-5 + 1 = 0/-5 + 1 = 1
Sum = (1/2)(-2 + -2) = 0
Therefore, the sum of the arithmetic sequence -2-7-2+ is 0.
4) The common difference in this arithmetic sequence is -4. To find the sum, we can use the formula:
Sum = (n/2)(first term + last term), where n is the number of terms.
First term = -3
Last term = -11
n = (last term - first term)/common difference + 1 = (-11 - (-3))/-4 + 1 = -8/-4 + 1 = 2 + 1 = 3
Sum = (3/2)(-3 + -11) = -21
Therefore, the sum of the arithmetic sequence -3-7-11 is -21.
5) The common difference in this arithmetic sequence is 4q. To find the sum, we can use the formula:
Sum = (n/2)(first term + last term), where n is the number of terms.
First term = 2q
Last term = 10q
n = (last term - first term)/common difference + 1 = (10q - 2q)/(4q) + 1 = 8q/4q + 1 = 2 + 1 = 3
Sum = (3/2)(2q + 10q) = (3/2)(12q) = 18q
Therefore, the sum of the arithmetic sequence 2q+6q+10q+ is 18q.