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Irina18 [472]
3 years ago
12

Write the first six terms of the arithmetic sequence with the given first​ term, a 1​, and common​ difference,

Mathematics
1 answer:
-Dominant- [34]3 years ago
3 0
a_1=a_1\\a_2=a_1+d\\a_3=a_2+d=a_1+2d\\a_4=a_3+d=a_1+3d\\a_5=a_4+d=a_1+4d\\a_6=a_5+d=a_1+5d
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Evaluate the series:<br> 2-10+50-250..., n=8
garik1379 [7]

The sum of first 8 terms of series is -130208

<em><u>Solution:</u></em>

Given that,

2 - 10 + 50 - 250 , ....

n = 8

Find the common ratio between a term and its previous term

r = \frac{-10}{2} = -5\\\\r = \frac{-250}{50} = -5

Thus common ratio is same

This is a geometric series

<em><u>The sum of terms of geometric sequence is given as:</u></em>

S_n = \frac{a_1(1-r^n)}{1-r}

Where,

r is the common ratio

n is the nth term

a_1 is the first term of series

From series,

a_1 = 2\\\\r = -5\\\\n = 8

Therefore,

S_8 = \frac{2 \times (1 - (-5)^8)}{1-(-5)}\\\\S_8 = \frac{2 \times (1-390625)}{6}\\\\S_8 = -130208

Thus sum of first 8 terms of series is -130208

6 0
4 years ago
Please help and EXPLAIN. Thank You!
Thepotemich [5.8K]
If I really understood the question, they ask the area of the small rectangle 3.5x2 . If so it's 7mm²
6 0
3 years ago
In the term -3k?mn, state the coefficient of <br>a) k²mn<br>b) -mn<br>c) 3k²<br><br>Help me please ​
kicyunya [14]

a) -3

b) 3k²

c) -mn

hope this helps

7 0
3 years ago
Brainlyest for the person who answers both and is right
svp [43]
123 x 10 to the -6 power
3 0
3 years ago
Read 2 more answers
Let f(x)=x^2 and g(x)=(x-3)^2+7 match up the correct transormations that are needed to transform the graph of f(x) to the graph
pentagon [3]

The transformations are vertical translation 7 units up.horizontal translation 3 units to the left

We have given that the equations

let f(x)=x^2 and g(x)=(x-3)^2+7

We have to determine the correct transformation,

<h3>What is the vertical translation?</h3>

Vertically translating a graph is equivalent to shifting the base graph up or down in the direction of the y-axis. A graph is translated to k units vertically by moving each point on the graph k units vertically.

Notice that the addition of 2 units to the variable x in the exponent involves a horizontal shift to the left in 2 units.

Notice as well that subtraction of 4 units to the functional expression involves a vertical shift downwards in 4 units.

To learn more about the transformation visit:

brainly.com/question/2689696

#SPJ1

5 0
2 years ago
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