# 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 - Mathematics

Sum

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.

#### Solution

Let the number of bacteria in a certain food = x

Since, they double in every second.

∴ x, 2x, 2(2x), 2(2 * 2 * x),...

i.e., x, 2x, 4x, 8x, ...

Now, let t_1 = x, t_2 = 2x , t_3 - 4x and t_4 = 8x

t_2 - t_1 = 2x - x = x

t_3 - t_2 = 4x - 2x = 2x

t_4 - t_3 = 8x - 4x = 4x

Since, the difference between each successive term is not same

So, the list does form an AP

Concept: Arithmetic Progression
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 5 Arithematic Progressions
Exercise 5.2 | Q 7.(iv) | Page 49
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