The first term of a sequence is -87. each successive term is created by adding 7 to its previous term. the number 165 is which numbered term in the sequence?

Step-by-step explanation:

The 36th sequence

Answer :  

The first term of a sequence is -87. 165 is 37th term of given Arithmetic sequence.

Solution:  

Given that ;

First term of the sequence  

Also each successive term is created by adding 7 to its previous term. This means given sequence is an arithmetic sequence with common difference d = 7.

Let’s say 165 be term of above arithmetic sequence that is = 165. We need to determine n.

Formula of term of arithmetic sequence is as follows:

where is the first term of the sequence

"d" is the common difference ratio

Substituting the given values we get

165 = -87 + (n-1) 7  

165 + 87 = 7n – 7

7n = 165 + 87 + 7  

n = = 37

Hence 165 is 37th term of given Arithmetic sequence.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

hreryryrranswer:

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