Question

Find the 10th partial sum of the arithmetic sequence defined by

Answer 1

Answer:

22.5

Step-by-step explanation:

If you expand the series, you can see the first few terms of the series:

• Putting 1 in $n$, $\frac{1}{2}(1)-\frac{1}{2}=0$
• Putting 2 in $n$, $\frac{1}{2}(2)-\frac{1}{2}=0.5$
• Putting 3 in $n$, $\frac{1}{2}(3)-\frac{1}{2}=1$
• Putting 4 in $n$, $\frac{1}{2}(4)-\frac{1}{2}=1.5$

We can see the series is 0, 0.5, 1, 1.5, ....

This is an arithmetic series with common difference (the difference in 2 terms) 0.5 and first term 0.

We know formula for sum of arithmetic series:

$s_{n}=\frac{n}{2}(2a+(n-1)d)$

Where,

• $S_{n}$ denotes the nth partial sum
• $a$ is the first term (in our case it is 0)
• $n$ is the term (in our case it is 10 since we want to find 10th partial sum -- sum until first 10 terms)
• $d$ is the common difference (difference in term and the previous term) (in our case it is 0.5)

Substituting these into the formula, we get the 10th partial sum to be:

$s_{10}=\frac{10}{2}(2(0)+(10-1)(0.5))\\s_{10}=5(0+(9)(0.5))\\s_{10}=5(0+4.5)\\s_{10}=5(4.5)\\s_{10}=22.5$

So the sum of the first 10 terms is 22.5. Third answer choice is right.

Answer 2

Answer is 22.5  so c :)