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The total number of coins required to fill all the boxes are
.
Further explanation:
In a chessboard there are boxes.
The objective is to determine the total number of coins required to fill the boxes in chessboard.
In the question it is given that in the first box there is coin, in the second box there are
coins, in the third box there are
coins and it continues so on.
A sequence is formed for the number of coins in different boxes.
The sequence formed for the number of coins in different boxes is as follows:
The above sequence can also be represented as shown below,
It is observed that the above sequence is a geometric sequence.
A geometric sequence is a sequence in which the common ratio between each successive term and the previous term are equal.
The common ratio for the sequence is calculated as follows:
The term of a geometric sequence is expressed as follows:
In the above equation is the first term of the sequence and
is the common ratio.
The value of and
is as follows:
Since, the total number of boxes are so, the total number of terms in the sequence is
.
To obtain the number of coins which are required to fill the boxes we need to find the sum of sequence formed as above.
The sum of terms of a geometric sequence is calculated as follows:
To obtain the sum of the sequence substitute for
,
for
and
for
in the above equation.
Therefore, the total number of coins required to fill all the boxes are
.
Learn more:
1. A problem on greatest integer function brainly.com/question/8243712
2. A problem to find radius and center of circle brainly.com/question/9510228
3. A problem to determine intercepts of a line brainly.com/question/1332667
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Sequence
Keywords: Series, sequence, logic, groups, next term, successive term, mathematics, critical thinking, numbers, addition, subtraction, pattern, rule., geometric sequence, common ratio, nth term.