Eric plays an online game called Gopher Invasion in which gophers emerge from holes in the ground to take over your farm. In the
1 answer:
Answer:
The required equation is B)
Step-by-step explanation:
Consider the provided information.
Let h is the number of holes which Eric needs to fill.
Eric fills 19 holes before the gophers take over and he loses.
There were still 24 holes left to fill in the first level.
That means Eric fill 19 holes and still need to fill 24 holes.
This can be written as:
Hence, the required equation is B)
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Answer:
A
Step-by-step explanation:
Recall that the sum of an arithmetic series is given by:
Where <em>n</em> is the number of terms, <em>a</em> is the first term, and <em>x</em>_<em>n</em> is the last term.
We know that the initial term <em>a</em> is 13, the common difference is 7, and the total sum is 2613. Since we want to find the number of terms, we want to find <em>n</em>.
First, find the last term. Recall that the direct formula for an arithmetic sequence is given by:
Since the initial term is 13 and the common difference is 7:
Substitute:
We are given that the initial term is 13 and the sum is 2613. Substitute:
Solve for <em>n</em>. Multiply both sides by two and combine like terms:
Distribute:
Simplify:
Isolate the equation:
We can use the quadratic formula:
In this case, <em>a</em> = 7, <em>b</em> = 19, and <em>c</em> = -5226. Substitute:
Evaluate:
Evaluate for each case:
We can ignore the second solution since it is negative and non-natural.
Therefore, there are 26 terms in the arithmetic series.
Our answer is A.