if the mean of 7 consecutive multiples of 3 is 18 find the fourth and fifth number
Answers
The fourth and fifth numbers are 18 and 21 respectively.
• Let the first multiple of 3 be x.
• There will be a difference of 3 between two consecutive multiples of 3.
=> The second multiple of 3 = x + 3
The third multiple of 3 = x + 3 + 3 = x + 6
The fourth multiple of 3 = x + 6 + 3 = x + 9
The fifth multiple of 3 = x + 9 + 3 = x + 12
The sixth multiple of 3 = x + 12 + 3 = x + 15
The seventh multiple of 3 = x + 15 + 3 = x + 18
• It is given that the mean of seven consecutive multiples of 3 = 18
=> (Sum of the seven consecutive multiples of 3) / 7 = 18
=> Sum of the seven consecutive multiples of 3 = 18 × 7 = 126
• x + (x + 3) + (x + 6) + (x + 9) + (x + 12) + (x + 15) + (x + 18) = 126
=> x + x + 3 + x + 6 + x + 9 + x + 12 + x + 15 + x + 18 = 126
=> 7x + 63 = 126
=> 7 (x + 9) = 126
=> x + 9 = 126 / 7
=> x + 9 = 18
=> x = 18 - 9
=> x = 9
• Therefore, the fourth number = 9 + 9 = 18
The fifth number = 9 + 12 = 21