Answer:
4480 meters.
Step-by-step explanation:
Every minute, the car's distance is being added by 120 meters constantly; which when represented with an arithmetic sequence:
280, 400, 520, ...
Since we are looking for the total distance in 7 minutes, we are simply going to be finding the sum of the first 7 terms in the sequence.
[tex]a_{1}[/tex] = 280 (first term)
[tex]d[/tex] = 120 (common difference)
[tex]n[/tex] = 7 (number of terms)
Then, we apply the arithmetic series formula.
Solution:
[tex]S_n &= \frac{n}{2} \cdot \left(2a_1 + (n-1) \cdot d \right) \\\\S_{ 7 } &= \frac{ 7 }{2} \cdot \left( 2 \cdot 280 + ( 7-1) \cdot 120 \right) \\S_{ 7 } &= \frac{ 7 }{2} \cdot \left( 560 + 6 \cdot 120 \right) \\S_{ 7 } &= \frac{ 7 }{2} \cdot \left( 560 + 720 \right) \\S_{ 7 } &= \frac{ 7 }{2} \cdot 1280 \\[/tex]
[tex]\boxed{S_{ 7 } &= 4480}[/tex]
#CarryOnLearning
