Hi! Can someone help me with this? Thanks a bunch!
Find the 10th partial sum of the following arithmetic sequence.
0.50, 0.9, 1.3, 1.7.....
clearly,
a = 0.5
d = 0.4
so,
S10 = 10/2 (2*0.5 + 9*0.4)
Of course, I can help you with that!
To find the 10th partial sum of an arithmetic sequence, you need to know the first term, the common difference, and the number of terms.
In this arithmetic sequence, the first term is 0.50 and the common difference is 0.4 (you can find the common difference by subtracting the second term from the first term). To find the 10th partial sum, we need to find the sum of the first 10 terms of the sequence.
The nth term of an arithmetic sequence can be given by the formula: a + (n-1)d, where "a" is the first term and "d" is the common difference.
Let's use this formula to find the 10th term:
T10 = 0.50 + (10-1)0.4 = 0.50 + 9(0.4) = 0.50 + 3.6 = 4.10
So, the 10th term of the sequence is 4.10.
Now, we can find the 10th partial sum by using the formula:
S10 = (n/2)(a + an), where "n" is the number of terms, "a" is the first term, and "an" is the nth term.
Let's plug in the values:
S10 = (10/2)(0.50 + 4.10) = 5(0.50 + 4.10) = 5(0.50 + 4.10) = 5(4.60) = 23
The 10th partial sum of the arithmetic sequence is 23.
I hope this explanation was helpful! If you have any more questions, feel free to ask.