Question 7 (iv)
In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers.
The number of bacteria in a certain food item after each second, when they double in every second.

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Solution

Letthe number of bacteria in a certain food be x.
Since, they double in every second, the series is:
$x, 2 x, 2 (2 x), 2 (2 (2 (x))), \dots$
$i . e x, 2 x, 4 x, 8 x, \dots$
$t_{2} - t_{1} = 2 x - x = x$
$t_{3} - t_{2} = 4 x - 2 x = 2 x$
$t_{4} - t_{3} = 8 x - 4 x = 4 x$
Since the difference between each successive term is not same, the list does not form an AP.

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Properties of AP

Standard X Mathematics

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Question 7 (iv) In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers. The number of bacteria in a certain food item after each second, when they double in every second.

Letthe number of bacteria in a certain food be x. Since, they double in every second, the series is: x,2x,2(2x),2(2(2(x))),… i.e x,2x,4x,8x,… t2−t1=2x−x=x t3−t2=4x−2x=2x t4−t3=8x−4x=4x Since the difference between each successive term is not same, the list does not form an AP.

Question 7 (iv)
In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers.
The number of bacteria in a certain food item after each second, when they double in every second.