# could anyone help on this question, pure year 2Watch

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#1

stuck on this question i dont understand why they r doing certain things in the answer,

i got a right and i got b right they were fairly straightforward
but with part c first i didnt understand that it would be year 1 + year 2 or just year 2 so it appears its year1 + year 2.

but the main part im stuck on is where they got this line from

520 × 52 + (11 + 22 + 33 + ...52 × 11)

i have the first year total commissions which is 13780, im not sure where they got 520*52 from ??? i thought if it was year 1 + year 2 itd just be 13780 + second years. and second years starts at 520 i believe, and increases by 11 each week, this is pretty confusing to me :/

so if i work out the second year total comissions which is (im sure):

531+(n-1)11 = 520+11n

a=520 [this is her starting amount of year 2]
d=11 [it changes from 10 each week to 11 each week]
n=52

52/2 (2*531 + (51)11)

that gives me
41626

and before this i tried

when typing this i tried a = 531 and it gives me the answer 42198 which is also the final answer of the actual answer, but i need to add year 1 to this so itd be more, so could anyone give me some directions on how to solve this, sequences n series has been the worst chapter so far, i guess ill have to spend more time on it
Last edited by anonymous230; 4 weeks ago
0
#2
ok i think my mistake is that i thought a was 520 but a is when n is one so that would be 531 right? and if i use 531 like i said i did above that gives me 42198 and i wouldnt have to add anything from year 1 to it and it is actually just asking me about year 2 only? cos thatd give me the right answer i guess, maybe solutionbank just confused me it does that sometimes, unless this is just a coincidence that it gives me that answer, could someone please clarify?
0
4 weeks ago
#3
(Original post by anonymous230)
ok i think my mistake is that i thought a was 520 but a is when n is one so that would be 531 right? and if i use 531 like i said i did above that gives me 42198 and i wouldnt have to add anything from year 1 to it and it is actually just asking me about year 2 only? cos thatd give me the right answer i guess, maybe solutionbank just confused me it does that sometimes, unless this is just a coincidence that it gives me that answer, could someone please clarify?
You are correct here.

The solution given in the Solution Bank is slightly misleading where for the solution to part c, the line that begins with "520 * 52" is really adding up each weeks commission in the second year (rather than the set-up on the preceding line, which states "Commision for year 1 policies + commission for year 2 policies").

For part c, we have for the second year:
- WEEK ONE: 520 + 11,
- WEEK TWO: 520 + (11 + 11),
- WEEK THREE: 520 + (11 + 2*11),
.
.
.

- WEEK n: 520 + (11 + (n-1)*11), where
(Note, the £520 in each weeks commission above is the commision from year one).

By adding up all the commission in year two, can you see where we get the "520 * 52" term from?
Last edited by simon0; 4 weeks ago
1
4 weeks ago
#4
(Original post by anonymous230)
52/2 (2*531 + (51)11)

that gives me
41626

...
This is giving me 42,198.
0
#5
(Original post by simon0)
This is giving me 42,198.
yeah i think i was meant to type 52/2 (2*520 + (51)11)

(Original post by simon0)
The solution given in the Solution Bank is slightly misleading where for the solution to part c, the line that begins with "520 * 52" is really adding up each weeks commission in the second year (rather than the set-up on the preceding line, which states "Commision for year 1 policies + commission for year 2 policies").
ahh that makes complete sense thanks a lot
0
#6
(Original post by simon0)

By adding up all the commission in year two, can you see where we get the "520 * 52" term from?
i still cant necessarily see it, do we substitute 52 = n into "520+(11 + n*11)" ?

oh unless its meant to be 520*(11+n*11)?

week 52 = 520 * (11 + 51*11)
week 52 = 520*52 ?

i can see it now, yes
0
4 weeks ago
#7
0
4 weeks ago
#8
(Original post by anonymous230)
i still cant necessarily see it, do we substitute 52 = n into "520+(11 + n*11)" ?

oh unless its meant to be 520*(11+n*11)?

week 52 = 520 * (11 + 51*11)
week 52 = 520*52 ?

i can see it now, yes
Not quite.

The formula for week n (in my original post) is the commission gained FOR THAT WEEK ONLY.

-----------------------------------------------------------------------------------------------------------

The question asks for the total commission for year 2.

Add up all the weeks commissions (of year 2):

S = "Week 1" + "Week 2" + ... + "Week 52",

= [520 + (11)] + [520 + (11 + 11)] + [520 + (11 + 2*11)] + ... + [520 + (11 + 51*11)],

= [520 + 11] + [520 + 22] + [520 + 33] + ... + [520 + (52 * 11)].

Then add up all the 520's (yes all 52 of them):

.

Then of course, as t is an arithmetic sequence (second term of S above), we can add up all the terms by using the summation formua:

t = (n/2)(2*a + (n-1)*d) = (52/2)(2*11 + (52-1)*11).

Then finally our total commision for year two (which is S) is just adding together (520 *52) with t.

-----------------------------------------------------------------------------------------

I made a mistake in my original post, the general formula for the week's commission for week n (in year 2) is:

520 + (11 + (n-1)*11)),

which is equivalent to: 520 + n*11.
Last edited by simon0; 4 weeks ago
0
#9
(Original post by simon0)
Not quite.

The formula for week n (in my original post) is the commission gained FOR THAT WEEK ONLY.

-----------------------------------------------------------------------------------------------------------

The question asks for the total commission for year 2.

Add up all the weeks commissions (of year 2):

S = "Week 1" + "Week 2" + ... + "Week 52",

= [520 + (11)] + [520 + (11 + 11)] + [520 + (11 + 2*11)] + ... + [520 + (11 + 51*11)],

= [520 + 11] + [520 + 22] + [520 + 33] + ... + [520 + (52 * 11)].

Then add up all the 520's (yes all 52 of them):

.

Then of course, as t is an arithmetic sequence (second term of S above), we can add up all the terms by using the summation formua:

t = (n/2)(2*a + (n-1)*d) = (52/2)(2*11 + (52-1)*11).

Then finally our total commision for year two (which is S) is just adding together (520 *52) with t.

-----------------------------------------------------------------------------------------

I made a mistake in my original post, the general formula for the week's commission for week n (in year 2) is:

520 + (11 + (n-1)*11)),

which is equivalent to: 520 + n*11.
oh ok yes i see it now much clearer, thanks so much for your time
0
4 weeks ago
#10
No problem.

If there are any more questions then ask away.
0
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