Question

Can someone check my work please?

Jared works for Bloom's Landscaping and will be planting a flower garden with rows of flowers. According to the plan, he will plant 6 plants in Row 1, 8 plants in Row 2, 10 plants in Row 3, and so on.

A) How many plants will be planted in Row 10? Show your work.

a) Rows 1/2/ 3 / 4 /5/ 6 / 7/ 8/ 9 / 10/11/12
Plants ->/6/8/10/12/14/16/18/20/22/24/26/28
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B) If the landscaper wants Jared to plant 12 rows of plants, how many plants will be needed?

b) 204 plants will be needed.
(to be continued)

Answer 1

C) If the landscaper purchased 300 plants, how many rows would JAred be able to make? How many plants, if any, would be left over?

C) I dont know how to do this one.
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D) If Jared started Row 1 with twice as many plants, (12 plants) and increased the number by 2 in each row, will Jared need twice as many plants as were needed in the original plan if 12 rows are planted?

d) i dont know how to do this one either.

Answer 2

how did you do part A?

Answer 3

I just went by two's @phi

Answer 4

do you know the formula for adding up N numbers:
0+1+2+3+...+N= N*(N+1)/2

if you go up by 2's we can tweak that formula

Answer 5

example:
0+1+2
here N=2 (last number) so the formula says the sum should be N*(N+1)/2 = 2*3/2= 3
and 1+2 = 3
it works. It will also work for all N

Answer 6

if we go up by 2:
0+2+4+6
that is like: 2(0+1+2+3) = 2*6= 12

so 2* sum of numbers from 0 to 3= 2* 6=12
is the fast way.

Answer 7

So for B it would be 12(6+28) divide it by 2 then

12(17) = 204?

Answer 8

if you have 12 rows:
6+0 + (6+2) + (6+4) + ... (6+22)

we can write that sum as
6+6+...+6 + 0+2+4+...+22
we have 12 6's
so that is
6*12 + 2(0+1+2+...+11)
simplify that

Answer 9

yes for B

Answer 10

I think for D we just multiply 204 with two right?

Answer 11

72 + 28 = 100

Answer 12

I think there is a formula to find the last term in a sequence.
then do the sum formula.

In other words, I would figure it out rather than try to intuit.

Answer 13

but it is clear if we start with 6 extra plants, we will have 6*12= 72 extra plants total added to the answer for part B

Answer 14

yes

Answer 15

thank you lol

Answer 16

Did you get part C ?

Answer 17

I think its 24 rows of plants would be needed and 52 left over?

Answer 18

@phi will you help me with a different question?

Answer 19

in a minute

Answer 20

the simplified formula for the sum of N rows (for your problem only)
seems to be (N+5)*N

so for 1 row: (1+5)*1= 6 works
for 2 rows : (2+5)*2 = 14 = 6+8 works
for 12 rows: (12+5)*12= 17*12= 204

so for part C:
(N+5)*N= 300
N^2 +5N-300 = 0
(N+20)(N-15)= 0
N= -20 can't use this
N= 15 this one works

Answer 21

in other words, exactly 15 rows, with no plants left over.