a bubble rises from the bottom of a pond to its surface by increasing its radius by 3 times its value when it was at the bottom.calculate the depth of the pond.(Hint: Pressure depends on the depth of the pond.Volume is inversely related to pressure.)[Science Olympiad]
Answers
Answer:
Explanation:Let the first term be a and the common difference be d
The sum of first term ,third term and fifth term is 39
⇒ a + ( a + 2d) + (a + 4d) = 39
⇒ a + a + 2d + a + 4d = 39
⇒ 3a + 6d = 39
⇒ a + 2d = 13 --------------------[ 1 ]
The sum of second term, 4th term and 6th term is 51
⇒ ( a + d) + (a + 3d) + (a + 5d) = 51
⇒ a + d + a + 3d + a + 5d = 51
⇒ 3a + 9d = 51
⇒ a + 3d = 17 --------------------[ 2 ]
Put the two equations together:
a + 2d = 13 --------------------[ 1 ]
a + 3d = 17 --------------------[ 2 ]
Equation [ 2 ] - [ 1 ] :
d = 4
Find a:
Sub d = 4 into equation 1
a + 2(4) = 13
a + 8 = 13
a = 5
Form the nth term:
an = a1 + (n - 1)d
an = 5 + (n - 1)4
an = 5 + 4n - 4
an = 4n + 1
Find the 10th term:
an = 4n + 1
a10 = 4(10) + 1
a10 = 41
Answer: The 10th term is 41