Answer: 742
Step-by-step explanation:
The given sequence {27, 31, 35, ... } provides the following information:
- the first term (a₁) = 27
- the difference (d) = 4
We can use the information above to find the explicit rule of the sequence:
[tex]a_n=a_1+d(n-1)\\.\quad =27+4(n-1)\\.\quad =27+4n-4\\.\quad =23+4n[/tex]
We can use the explicit rule to find the 14th term (a₁₄)
[tex]a_n=23+4n\\a_{14}=23+4(14)\\.\quad =23+56\\.\quad =79[/tex]
Next, we can input the first and last term of the sequence into the Sum formula:
[tex]S_n=\dfrac{a_1+a_n}{2}\times n\\\\S_{14}=\dfrac{a_1+a_{14}}{2}\times 14\\\\.\quad =\dfrac{27+79}{2}\times 14\\\\.\quad =\dfrac{106}{2}\times 14\\\\.\quad =53\times 14\\\\.\quad =742[/tex]
