Arithmetic and Geometric Sequences 1. Consider the sequence: 3, 7, 11, 15...

Find an explicit formula for the n-th term of this sequence.
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Step-by-step explanation:

This is arithmetic since adding 4 to each term gets us to the next term in the sequence. That means that the common difference, d, is 4. The general arithmetic explicit formula is

and using the info given when a1 = 3 and d = 4:

or, if you want to make it easier to deal with:

(I just distributed through the parenthesis and then combined like terms. As you can see, arithmetic sequences are linear).

answer: 140

step-by-step explanation:

so just add all then it will be your answer but i am not pretty sur eif it is but hope this i am here to people

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is