Question

What is the sum of the first 18 terms of the arithmetic series `11+15+19+23+...`?

Answer 1

`810`

Explanation:

The required formula is `color(red)(S_n = n/2[2a +(n-1)d])`

Where,

`S_n` is the sum of `n` terms
`n`= the number of terms, `" "n=18`
`a` = the first term, `color(white)(xxxxxxx)a = 11`
`d=` the common difference, `" "d= 4`

Substituting these values gives:

`S_18 = 18/2[2(11)+(18-1)(4)]`

`= 9[22+17xx4]`

`=9[22+68]`

`=9[90]`

`=810`