Aprilajace2idn
Answered

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1. A car travels 280 meters in first minute, 400 meters in the next minute, 520 meters in the third
minute, and so on. What is the total distance of the car travels in 7 minutes at the same rate?​

Sagot :

Xivxburnidn

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]

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