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3 years ago

If an arithmetic sequence has a4 = 107 and a8 = 191, what is a₁?PLEASE HELP ME

Mathematics

1 answer:

katen-ka-za [31]3 years ago

3 0

$\text{nth term of an arithmetic sequence,}\\\\a_n = a_1 + (n-1)d\\\\a_4 = a_1 +3d=107~~~......(i)\\ \\a_8=a_1+7d = 191~~~......(ii)\\\\\\\text{(ii) -(i):}\\\\~~~~~~a_1+7d-a_1-3d = 191 -107\\\\\implies 4d = 84\\\\\implies d = \dfrac{84}4\\\\\implies d= 21\\\\\text{Substitute d= 21 in eq~(i):}\\ \\~~~~~ a_1 +3(21) = 107\\\\\implies a_1 + 63 = 107\\\\\implies a_1 = 107-63\\\\\implies a_1 =44$

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Given equation is y =7x - 5.

Let's plug in the values of x's to get their corresponding values of y's.

Let's plug in x = -5. So,

y = 7( -5) - 5 = -35 - 5 = -40

So, the first order pair is (-5, -40)

Hence, the first choice is not correct.

For x = 2, y = 7 (2) - 5 = 14 - 5 = 9.

Second order pair is (2, 9). So, second choice is also not correct.

Now for x = 0, y = 7(0) - 5 = - 5.

So, the third order pair is (0, -5).

Let's plug in x = -3 to check the third order pair list as we have already got two order pair (0, -5) and (2, 9) from that list.

For x = -3, y = 7(-3) - 5 = - 21 - 5 = -26.

Hence the correct choice is {(0, −5), (2, 9), (−3, −26)}.

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3 years ago

A function is represented by the set of ordered pairs shown below.

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Answer: {3, 5, 7}

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The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input. The output values are y = 3, y = 3, y = 3, y = 5, y = 7. So we simply list these outputs without the "y=" portion. Toss out any duplicates. Only write the unique output values.

The curly braces surrounding the list of values tells us that we have a set.

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3 years ago

If an arithmetic sequence has a4 = 107 and a8 = 191, what is a₁?PLEASE HELP ME​

If an arithmetic sequence has a4 = 107 and a8 = 191, what is a₁?PLEASE HELP ME