the average of 50 consecutive natural number is X what will be the new average when the next four natural number are also included
Answers
Answer:
X + 2
Step-by-step explanation:
Let the no. be x₁ , x₂ , x₃ ......... x₅₀.
Therefore, (x₁ + x₂ + x₃ + .........+ x₅₀) / 50 = X
x₁ + x₂ + x₃ + .........+ x₅₀ = 50 X
But we know that they are consecutive no.
∴, x₂ = x₁ + 1
x₃ = x₁ + 2(1) = x₁ + 2 ....
x₅₀ = x₁ + 49
∴, x₁ + x₂ + x₃ + .........+ x₅₀ = 50 X
x₁ + x₁ + 1 +x₁ +2 + x₁ + 3 ... + x₁ + 49 = 50 X
50 (x₁) + 1 + 2 + 3 + ... + 49 = 50 X
50 x₁ + 1225 = 50 X
x₁ = (50 X - 1225) / 50
If 4 more no. are added, new sum =
x₁ + x₂ + x₃ + ... +x₅₄
(x₁ + x₂ + x₃ + ... +x₅₀) + x₅₁ + x₅₂ + x₅₃ + x₅₄
50 X + x₁ + 50 + x₁ + 51 + x₁ + 52 + x₁ + 53
50 X + 4 x₁ + 206
50 X + 4 [(50 X - 1225) / 50] + 206
50 X + 4 X - 98 + 206
54 X + 108
∴, Average = Sum / No. of terms
= (54 X + 108) / 54
= X + 2