Solve for x and explain the steps in your answer. Please Help :/
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Perimeter of a shape is the total length of its border
Figure 1, perimeter = 5 units
Figure 2, perimeter = 7 units
Figure 3, perimeter = 9 units
Figure 4, perimeter = 11 units
Notice that the perimeter is forming an Arithmetic sequence; 5, 7, 9, 11 with a common difference of 2
The general form of an Arithmetic sequence is
Where 'd' is a common difference and 'n' is the number of terms.
We have d = 2, and
zero term = the term before the first term = 3
⇒ This is the rule to find the perimeter of the next figures
Figure 1, perimeter = 5 units
Figure 2, perimeter = 7 units
Figure 3, perimeter = 9 units
Figure 4, perimeter = 11 units
Notice that the perimeter is forming an Arithmetic sequence; 5, 7, 9, 11 with a common difference of 2
The general form of an Arithmetic sequence is
Where 'd' is a common difference and 'n' is the number of terms.
We have d = 2, and
zero term = the term before the first term = 3
Notice that
13 - 9 = 4
17 - 13 = 4
so it's likely that each pair of consecutive terms in the sum differ by 4. This means the last term, 149, is equal to 9 plus some multiple of 4 :
149 = 9 + 4k
140 = 4k
k = 140/4
k = 35
This tells you there are 35 + 1 = 36 terms in the sum (since the first term is 9 plus 0 times 4, and the last term is 9 plus 35 times 4). Among the given options, only the first choice contains the same amount of terms.
Put another way, we have
but if we make the sum start at k = 1, we need to replace every instance of k with k - 1, and accordingly adjust the upper limit in the sum.