The common difference is d = 4 because we add 4 to each term to get the next one.
The starting term is a1 = 3
The nth term of this arithmetic sequence is
an = a1 + d(n-1)
an = 3 + 4(n-1)
an = 3 + 4n-4
an = 4n - 1
Plug in n = 25 to find the 25th term
an = 4n - 1
a25 = 4*25 - 1
a25 = 100 - 1
a25 = 99
So we're summing the series : 3+7+11+15+...+99
We could write out all the terms and add them all up. That's a lot more work than needed though. Luckily we have a handy formula to make things a lot better
The sum of the first n terms is Sn. The formula for Sn is
Sn = n*(a1+an)/2
Plug in n = 25 to get
Sn = n*(a1+an)/2
S25 = 25*(a1+a25)/2
Then plug in a1 = 3 and a25 = 99. Then compute to simplify
S25 = 25*(a1+a25)/2
S25 = 25*(3+99)/2
S25 = 25*(102)/2
S25 = 2550/2
S25 = 1275
The final answer is 1275
Hope this picture helps you
y =x^2 +3
to find the inverse interchange the x and y and solve for y
x = y^2 +3
subtract 3 from each side
x-3 = y^2
take the sqrt of each side
+-sqrt(x-3) =y
Answer:
20
Step-by-step explanation:
First step is finding an angle in the rightmost triangle (angle K)
Using TOA we have
Tan(x)=4/8
x=26.565
which means that 90-26.565= 63.4349 will give us angle K in regards to the left triangle
Using this we can solve for JM
Tan(63.4349)=x/8
8tan(63.4349=x
x=16
So if JM = 16
and LM=4
take their sum to find JL
16+4=20