Since we know this is an arithmetic sequence, to find the number of terms, it will be helpful to find the distance d between every term.
d = 1616 - 1313
d = 303
now let's think about how to generate the nth term of an arithmetic sequence given the first term 1313 and distance d.
second term = d + 1313
third term = second term + d
third term = 1313 + 2d
fourth term = third term + d
fourth term = 1313 + 3d
we are starting to see a pattern:
nth term = 1313 + (n-1)d
we know this pattern will continue because we are simply adding d to the previous term to get the next term so if the previous term n - 1 was 1313 + d(n - 2), then the next term n will be 1313 + d(n-1). to put i simply, since the first term was 1313, we know the 2nd term must be 1313 + d and since the 2nd term is 1313 + d, we know the third term must be 1313 + 2d and so on until the nth term which is 1313 + (n-1)d. we know the nth term of this sequence is 7373 and we know that d is 303 so:
7373 = 1313 + 303(n-1) and we just have to solve for n.
doing so gives:
n = 21 terms
let me know if you have any questions!
Answer:
92
Step-by-step explanation:
Multiplying two negatives together results in a positive.
-23 * -4 = 23 * 4 = 92
answer:m3+27n3
Step-by-step explanation:
Rewrite
27
n
3
as
(
3
n
)
3
.
m
3
+
(
3
n
)
3
Since both terms are perfect cubes, factor using the sum of cubes formula,
a
3
+
b
3
=
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
where
a
=
m
and
b
=
3
n
.
Answer:
(-22, -18)
Step-by-step explanation:
Midpoint=(
you already know the midpoint, so you're kind of working backward.
Midpoint (-2, 4)
you'll need to work each part of the equation separately to find x and y
x first
-2=
solve for x
multiply both sides by 2
-4 = x+18
subtract (18) from both sides
-22 = x
now y
4=
solve for y
multiply both sides by 2
8 = y+26
subtract 26
y = -18
second endpoint (-22, -18)
Answer:
3/4
Step-by-step explanation: