Question

A diver was collecting water samples from a lake he collected a sample at every interval of 3 m starting at 5 m below the water surface. the final samples was collected at a depth of 35 m. how many samples did he collect​

Answer 1

Given data : A diver was collecting water samples from a lake he collected a sample at every interval of 3 m starting at 5 m below the water surface. the final samples was collected at a depth of 35 m.

To find : How many samples did he collect ?

Solution :

Here we use arithmetic progression to find number of collected samples.

Now,

${\implies{a_{n} = a + (n - 1) \times d}}$

Where,

• a = First term = 5 m (starting)
• d = Common difference = 3 m (every interval)
• n = number of terms = collected samples at every interval = ?
• a_n = n'th term = 35 m (final depth)

⟹ 35 = 5 + (n - 1) * 3

⟹ 35 - 5 = (n - 1) * 3

⟹ 30 = (n - 1) * 3

⟹ 30 = 3n - 3

⟹ 3n = 30 + 3

⟹ 3n = 33

⟹ n = 33/3

⟹ n = 11

Answer : The samples collected by the diver are 11.