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 35m . How many samples did he collect?,
Answers
The easiest method would be using A.P (hope you have learnt it )
Represent the given data in series like given below:
A.P: 5,8,11..........,35
According to the A.P formula we have;
＜ an= a+ (n-1)d ＞
Here,
a=5 (distance at which first sample is collected/the first term)
an= 35 (distance at which last sample is collected/last term)
d= secound term - first term
=8-5=3 (interval at which sample is collected)
n= no of samples collected,which is what we need to find
Substitute all the values in the formula
We get,
an=a+(n-1) × d
35=5+(n-1) × 3
30=(n-1)×3
30=3n-3
33=3n
11=n
Which is the required number of samples collected.
Hence at the end of 35m 11 samples will be collected.
Here,
a=5 (distance at which first sample is collected/the first term)
an= 35 (distance at which last sample is collected/last term)
d= secound term - first term
=8-5=3 (interval at which sample is collected)
n= no of samples collected,which is what we need to find
Substitute all the values in the formula
We get,
an=a+(n-1) × d
35=5+(n-1) × 3
30=(n-1)×3
30=3n-3
33=3n
n = 11