Answer: $25,500
Step-by-step explanation:
The given sequence {1300, 1300+150, ... } provides the following information:
- the first term (a₁) = 1300
- the difference (d) = 150
We can use the information above to find the explicit rule of the sequence:
[tex]a_n=a_1+d(n-1)\\.\quad =1300+150(n-1)\\.\quad =1300+150n-150\\.\quad =1150+150n[/tex]
We can use the explicit rule to find the 12th term (a₁₂)
[tex]a_n=1150+150n\\a_{12}=1150+150(12)\\.\quad =1150+1800\\.\quad =2950[/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_{12}=\dfrac{a_1+a_{12}}{2}\times 12\\\\.\quad =\dfrac{1300+2950}{2}\times 12\\\\.\quad =\dfrac{4250}{2}\times 12\\\\.\quad =2125\times 12\\\\.\quad =25,500[/tex]
