Find the sum of the first 90 terms of the sequence -4,-1,2,5,8
1 answer:
Answer:
1655
Step-by-step explanation:
Note the common difference d between consecutive terms of the sequence
d = - 1 - (- 4) = 2 - (- 1) = 5 - 2 = 8 - 5 = 3
This indicates the sequence is arithmetic with sum to n terms
=
[ 2a₁ + (n - 1)d ]
Here a₁ = - 4, d = 3 and n = 90, thus
=
[ (2 × - 4) + (89 × 3) ] = 45(- 8 + 267) = 45 × 259 = 1655
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<h2>Answer: slope = - 95</h2><h2>
</h2>
Step-by-step explanation:
The question gives us two points, (87, 91) and (88, -4), from which we can find the slope and later the equation of the line.
<u> </u>
<u>Finding the Slope</u>
The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)
= (91 - (- 4)) ÷ (87 - 88)
= - 95
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<em><u>Checking my answer:</u></em>
<em>Finding the Equation</em>
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - (-4) = - 95 (x - 88)
y + 4 = - 95 (x - 88)
<em>To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.</em>
Given:
The equation of the parabola is:
To find:
The y-intercept of the parabola.
Solution:
We have,
Putting in the given equation, we get
Therefore, the y-intercept of the parabola is 0. It means the y-intercept of the given parabola is at point (0,0).