Question

PLEASE HELP
Pat found the average of the first 2021 positive even integers and Lee found the average of the first 2021 positive odd integers how much greater is pat's average than lee's?

Answer 1

Answer:

1 greater

Step-by-step explanation:

Answer 2

Pat's average is greater that Lee's average by 2021.

To find,

how much greater is pat's average than lee's

Solution:

Let's find average of the first 2021 positive even integers. The series is an A.P

• 2,4...., tn

The sum of all terms of an A.P is

• S = n/2[2a + (n − 1) × d]

Here,

• n1=2021
• a1=2
• d1=2

Hence,

• S1 = 2021/2[2(2) + (2021− 1) × 2]
• S1 = 2021/2 [4+4002]
• S1 = 2021/2 [4006]
• S1 = 2021×2003
• S1 = 4,048,063

Let's find average of the first 2021 positive odd integers. The series is also an A.P

• 1,3...., tn

The sum of all terms of an A.P is

• S = n/2[2a + (n − 1) × d]

Here,

• n2=2021
• a2=1
• d2=2

Hence,

• S2 = 2021/2[2(1) + (2021− 1) × 2]
• S2 = 2021/2 [2+4002]
• S2 = 2021/2 [4004]
• S2 = 2021×2002
• S2 = 4,046,042

The difference between S1 and S2 is 2021.

Hence, Pat's average is greater that Lee's average by 2021.

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