Question

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

Answer 1

Answer is 22.5 so c :)

Answer 2

22.5

Explanation:

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

• Putting 1 in
  `n`,
  `(1)/(2)(1)-(1)/(2)=0`
• Putting 2 in
  `n`,
  `(1)/(2)(2)-(1)/(2)=0.5`
• Putting 3 in
  `n`,
  `(1)/(2)(3)-(1)/(2)=1`
• Putting 4 in
  `n`,
  `(1)/(2)(4)-(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)=(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)=(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.