Answer:
287
Step-by-step explanation:
Sum of A Finite Arithmetic Sequnece is
[tex] \frac{a _{1} + a _{n} }{2} n[/tex]
Where a1 is first term
an is final term
N is the number of terms.
We know a1 is 1
An is 40 but we don't know n.
To find n, we use the definition of a Arithmetic Sequence
[tex]a _{n} = a + (n - 1)d[/tex]
where d is the common difference. Let use the final term, 40 as a example.
Here the common difference is 3 so we have
[tex]40= 1 + (n - 1)3[/tex]
[tex]39 = 3(n - 1)[/tex]
[tex]13 = n - 1[/tex]
[tex]14 = n[/tex]
So we have 14 terms in this finite series.
Now we compute
[tex] \frac{1 + 40 }{2}(14) = \frac{41}{2} (14) = 41 \times 7 = 287[/tex]
So the answer is 287
