$a)\\\\
a_{n+1}-a_n=d\\
for\ n=1\\
a_2-a_1=d\\
d=3-1=2\ - difference\ between\ two\ consecutive\ terms\\\\
b)\\
a_n=a_1+(n-1)d\\
n=101\\
a_{101}=1+(101-1)*2\\
a_{101}=1+100*2=200+1=201\\\\
c)\\
Sn=\frac{a_1+a_n}{2}*n\\
n=20\\
a_n=a_{20}=1+(20-1)*2=1+38=39\\
Sn=\frac{1+39}{2}*20=400\ \ Sum\ of\ the\ first\ 20 \ numbers.$

6 0

3 years ago

Given the differential Equation y'+2y=2e^x ;solve this equation using the integration factor; solve for y to get the general sol

SCORPION-xisa [38]

$y'+2y=2e^x\Longrightarrow y'=2e^x-2y$

If $f'(x)=g(x)$ then $y=\int{g(x)dx}$

So we extract,

$y=\int{2e^x-2x}dx$

Which becomes,

$y=2e^x-x^2+C$

Hope this helps.

r3t40

5 0

3 years ago

How can you use the properties of operations to evaluate this expression? 18 + 4(28)

nirvana33 [79]

Answer:

Well on of the properties states that unless there are parenthesis, you multiply and divide first then you add and subtract. So, first we multiply 28*4 and that leaves use with 112, now if there is no more multiplication, division, or parentheses, and there's not. We can continue all we do is add 18+112 and we get our answer of 130.

6 0

2 years ago

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