Number of shaded triangles in the first figure = 1
Number of shaded triangles in the second figure = 3
Number of shaded triangles in the third figure = 9
If we observe these values, we can conclude that a Geometric Series is being formed.First number is multiplied by 3 to get the second number and second number is multiplied by 3 to get the third number. So the summation can be expressed using the Geometric Series.
The summation uses the general term to express the sum over the interval. So first we find the general term of geometric series.
First term of the series = 1
Common ratio = 3
So, the general term of the series will be: [tex]1(3)^{n-1} [/tex]
This general term gives the terms of given geometric series for different values of n. For n = 1, we will have the first term which will is 1. Similarly for n=2, we will have the second term which is 3.
So the summation will start with first term and end on 15th term. Therefore, correct summation for this case is expressed by first option.
