The number of bacteria in a certain food item after each second, when they double in every second, do the lists of numbers involved form an AP
Solution:
An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. It is obtained by adding the same fixed number to its previous term.
Let the number of bacteria present in food initially be x.
Since, they double in every second , x, 2x, 2(2x), 2(2 . 2 . x),…= x, 2x, 4x, 8x,…
From the question given,
t₁ = x,
t₂ = 2x,
t₃ = 4x
t₄ = 8x.
Calculating the difference,we get,
t₂ - t₁ = 2x - x = x
t₃ - t₂ = 4x - 2x = 2x
t₄ - t₃ = 8x - 4x = 4x.
Hence, the difference between each successive term is not the same.
Therefore, the list does not form an AP.
✦ Try This: If the sum of first 7 terms of an A.P is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.2 Problem 7 (iv)
The number of bacteria in a certain food item after each second, when they double in every second, do the lists of numbers involved form an AP
Summary:
The number of bacteria in a certain food item after each second, when they double in every second does not form an A.P
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