Question

Modern car company has come out with a new car model. Market analysts predict that 4,600 cars will be sold in the first month and that sales will drop by 50 cars per month after that during the first year. Write out the first five terms of the​ sequence, and find the number of sold cars predicted for the twelfth month. Find the total predicted number of sold cars for the first year.

Answer 1

The first five terms of the sequence are; 4,600, 4,550, 4,500, 4,450, 4,400 and the total predicted number of sold cars for the first year is 51,900 cars

Arithmetic sequence

• First month, a = 4,600 cars
• Common difference, d = -50 cars

First five terms;

a = 4,600

a + d = 4600 + (-50)

= 4600 - 50

= 4,550

a + 2d

= 4600 + 2(-50)

= 4600 - 100

= 4,500

a + 3d

= 4,600 + 3(-50)

= 4,600 - 150

= 4,450

a + 4d

= 4600 + 4(-50)

= 4,600 - 200

= 4,400

cars predicted for the twelfth month.

a + 11d

= 4600 + 11(-50)

= 4600 + 550

= 4,050

Total predicted number of sold cars for the first year:

Sn = n/2{2a + (n - 1)d }

= 12/2{2×4600 + (12-1)-50}

= 6{9200 + 11(-50)}

= 6(9,200 - 550)

= 6(8,650)

= 51,900 cars

Learn more about arithmetic sequence:

brainly.com/question/6561461

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