Question

Write the sum using summation notation, assuming the suggested pattern continues.

-1 + 2 + 5 + 8 + ... + 44

Answer 1

The numbers increase by 3 starting at 0 use the equation for arithmetic sequence.

n
∑ 3x-1
i = 0


proper notion is shown in the picture.

Answer 2

345

Explanation:

We know that
`1+2+3+...+n=(n(n+1))/(2)`

Given pattern :
`-1 + 2 + 5 + 8 + ... + 44`

-1 + 2 + 5 + 8 + ... + 44 = \sum_{i=0}^{15} 3x-1

We can write
`\sum_(i=0)^(15) 3x-1=3\sum_(i=0)^(15)x-\sum_(i=0)^(15)1`

Here,
`3\sum_(i=0)^(15)x=3\left ( 1+2+3+...+15 \right )`

On putting n = 15 in
`(15(15+1))/(2)=(15* 16)/(2)=120`

So,
`3\sum_(i=0)^(15)x=3(120)=360`

Also,
`\sum_(i=0)^(15)1=15`

Therefore,

`-1 + 2 + 5 + 8 + ... + 44\\=\sum_(i=0)^(15) \left ( 3x-1 \right )\\=3\sum_(i=0)^(15)x-\sum_(i=0)^(15)1\\=3\left ( 0+1+2+3+...+15 \right )-15\\=3\left [ (15\left ( 15+1 \right ))/(2) \right ]-15\\=360-15\\=345`