Question

Please Help! Riley was determined to be on the basketball team. He started practicing for 40 minutes on the first day, and then increased his practice time by 20 minutes on each subsequent day. With that pattern, how many total minutes will he have practiced in 25 days?

Answer 1

Answer:

Correct answer:  pt = 7,000 minutes

Step-by-step explanation:

This is arithmetic series:

p₁ = 40 min

p₂ = p₁ + 20

p₃ = p₂ + 20 = p₁ + 2 · 20

p₄ = p₃ + 20 = p₁ + 3 · 20

...........................................

pₙ = p₁ + (n - 1) · 20

25 - th day will be practicing:

p₂₅ = 40 + 24 · 20 = 520 minutes

The total sum of the arithmetic series is calculated according to the following formula:

Sₙ = (n/2) (p₁ + pₙ)

In 25 days he will have practiced total minutes

pt = (25/2) · ( 40 + 520) = (25/2) · 560 = 7,000 minutes

pt = 7,000 minutes

God is with you!!!

Answer 2

Answer: he would have practiced for 7000 minutes in 25 days.

Step-by-step explanation:

His practice time is increasing in arithmetic progression each day. The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

Where

n represents the number of terms in the arithmetic sequence.

d represents the common difference of the terms in the arithmetic sequence.

a represents the first term of the arithmetic sequence.

From the information given,

a = 40 minutes

d = 20 minutes

For minutes practiced in 25 days,

n = 25

Therefore, the sum of the first 25 terms, S205 would be

S25 = 25/2[2 × 40 + (25 - 1)20]

S25 = 12.5[80 + 480)

S25 = 12.5 × 560 = 7000