Find the 10th partial sum of the arithmetic sequence defined by (An)={1/2n-1/2}
no, how did you get 4.5 ???
sum(10) = 5(0 + 9(1/2))
= 5(4.5)
= 22.5
1. D 42.5
2. A s9=9/2(2+26)
3. B 22.5
4. D 617.5
5. A 425.25
a(1) = (1/2)(1) - 1/2 = 0
a(2) = (1/2)(2) - 1/2 = 1/2
a(3) = (1/2)(3) - 1/2 = 1
....
looks like an arithmetic sequence with a = 0, d = 1/2
sum(n) = (n/2)(2a + (n-1)d )
your turn .....
If An is arthimetic sequence with A1=5, A5=21 find partial sum s30, An is equal to...
Step 1: Find the common difference:
d = (A5 - A1)/(5 - 1) = 4
Step 2: Find the nth term formula:
An = A1 + (n-1)d
Step 3: Use the nth term formula to find A30:
A30 = 5 + (30-1)(4) = 117
Step 4: Use the sum formula to find the partial sum S30:
S30 = (30/2)(A1 + A30)
S30 = (15)(5 + 117)
S30 = 1815
Therefore, the partial sum S30 of the arithmetic sequence with A1 = 5 and A5 = 21 is 1815. The nth term formula is An = 5 + (n-1)4.
To find the 10th partial sum of the arithmetic sequence defined by (An)={1/2n-1/2}, we need to add up the first 10 terms of the sequence.
The nth term of an arithmetic sequence is given by the formula An = a + (n-1)d, where a is the first term and d is the common difference. In this case, a = 1/2 and d = -1/2.
Let's calculate the first 10 terms of the sequence:
A1 = 1/2 + (1-1)(-1/2) = 1/2
A2 = 1/2 + (2-1)(-1/2) = 0
A3 = 1/2 + (3-1)(-1/2) = -1/2
A4 = 1/2 + (4-1)(-1/2) = -1
A5 = 1/2 + (5-1)(-1/2) = -3/2
A6 = 1/2 + (6-1)(-1/2) = -2
A7 = 1/2 + (7-1)(-1/2) = -5/2
A8 = 1/2 + (8-1)(-1/2) = -3
A9 = 1/2 + (9-1)(-1/2) = -7/2
A10 = 1/2 + (10-1)(-1/2) = -4
Now, let's find the sum of these 10 terms:
S10 = A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8 + A9 + A10
= 1/2 + 0 + (-1/2) + (-1) + (-3/2) + (-2) + (-5/2) + (-3) + (-7/2) + (-4)
By simplifying the expression, we get:
S10 = -41/2
Therefore, the 10th partial sum of the arithmetic sequence defined by (An)={1/2n-1/2} is -41/2.