Question

Find the sum to 40 terms of the arithmetic sequence below. Please show your work. 14+23+32

Answer 1

Answer:

7580

Step-by-step explanation:

The formula for the sum of an arithmatic sequence is

$\frac{n}{2} (a_{1} + a_{n})$,

where n = total number of terms (in this case 40)

$a_{1}$= the first term (in this case 14)

and $a_{2}$ = the last term (we will need to find this)

to find the last term, we can use this formula:

$a_{n} = a_{1} + (n-1)d$

where d is the difference between each term (in this case 9, because 23 - 14 = 9, and 32 - 23 = 9)

thus, $a_{n}$ = 14 + (40 - 1)9 = 14 + 39*9 = 14 + 351 = 365

plug this back into the first formula to get

Σ = $\frac{40}{2}$ (14 + 365) = 20(379) = 7580