Respuesta :
The river level raises by 49152 inches in 15 days.
Solution:
The river rose three inches the first day, and each day twice as much as the previous day. Â
We have to find how much did the river rise in fifteen days
Now, let the normal level be "n", then, first day level will be n + 3 inches
So 1st day raise will be 3
And second day raise will be 2(3)
Now, 3rd day raise will be [tex]2(2(3)) \rightarrow(3) 2^{2}[/tex]
So, this forms geometric progression
A geometric sequence is a sequence with the ratio between two consecutive terms is constant
[tex]\text { (3) },(3)2^1 ,(3) 2^{2} \dots \ldots \ldots[/tex]
with first term a = 3 and common ratio "r" = 2
Now, we have to find raise after 15 days
[tex]\text { We have to find } \mathrm{t}_{15} \text { of G.P }[/tex]
The nth term of G.P is given as:
[tex]t_{n}=a \cdot r^{n-1}[/tex]
[tex]\begin{array}{l}{t_{15}=3 \times(2)^{15-1}} \\\\ {=3 \times 2^{14}} \\\\ {=3 \times 16384=49152}\end{array}[/tex]
Hence, the river level raise by 49152 inches in 15 days.
