Answer:
Step-by-step explanation:
1) since the sixth term is 3 and the fifth term 24, the common ratio would be 3/24 = 1/8
The formula for finding the nth term of a geometric sequence is
Tn = ar^(n - 1)
If t6 = 3,r = 1/8, then
3 = a × 1/8^(6 - 1) = a × (1/8)^5
a = 3/(0.125)^5 = 98304
The first term is 98304.
Second term is 98304 × 1/8 = 12288
Third term is 12288 × 1/8 = 1536
Third term is 1536 × 1/8 = 192
2) t1 = 4
t2 = - 3t(2- 1) = - 3t1 = - 3 × 4 = - 12
t3 = - 3t(3- 1) = - 3t2 = - 3 × - 12 = 36
t4 = - 3t(4- 1) = - 3t3 = - 3 × 36 = - 108
3) let the numbers be t2,t3 and t4
The sequence becomes
1/2, t2,t3, t4,8
The formula for finding the nth term of a geometric sequence is
Tn = ar^(n - 1)
8 = 1/2 × r^(5 - 1)
8 = 1/2 × r^4
16 = r^4
2^4 = r^4
r = 2
t2 = 1/2 × 2 = 1
t3 = 1 × 2 = 2
t4 = 2 × 2 = 4
Number of sweaters bought by Jocelyn = 2
Price of the 2 sweaters including tax and discount coupon = 23.56
Amount of ales tax taken = 1.36
Amount of discount coupon = 5.00
Then
Price of 2 sweaters before tax = 23.56 - 1.36
= 22.20
Then
Price of the sweater before discount coupon was applied = 22.20 + 5.00
= 27.20
So
Price of 1 sweater before tax and coupon discount = 27.2/2
= 13.6
So the price of 1 sweater before tax and coupon discount is 13.6.
6 - x = 2(x - 6)
the first step, following PEMDAS, is to distribute the 2 to the inside of your parentheses:
6 - x = 2x - 12 ... subtract 2x
6 - 3x = -12 ... subtract 6
-3x = -18 ... divide by -3
x = 6 is the answer
Abcdefghijklmnopqrstuvwxyz
ok
b to a
goes back 1 letter
then b to d
skips 3 letters forward
then d to e
1 forward
e to h
skips 3 forward
h to g
goes 1 back
g to k
goes 3 forward
pattern seems to be
1back, 3 forward, 1 forward, 3 forward, repeat
so we are at 3 forward after than 1 back, so the next one is 1 forward
1 forward from k is l
the next letter is L
