Answer:
7580
Step-by-step explanation:
The formula for the sum of an arithmatic sequence is
[tex]\frac{n}{2} (a_{1} + a_{n})[/tex],
where n = total number of terms (in this case 40)
[tex]a_{1}[/tex]= the first term (in this case 14)
and [tex]a_{2}[/tex] = the last term (we will need to find this)
to find the last term, we can use this formula:
[tex]a_{n} = a_{1} + (n-1)d[/tex]
where d is the difference between each term (in this case 9, because 23 - 14 = 9, and 32 - 23 = 9)
thus, [tex]a_{n}[/tex] = 14 + (40 - 1)9 = 14 + 39*9 = 14 + 351 = 365
plug this back into the first formula to get
Σ = [tex]\frac{40}{2}[/tex] (14 + 365) = 20(379) = 7580
