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C1 Sequence, I have the written solutions but don't understand one of the solutions.

I have attached an image of both the question and written solution. It is part C, which I have circled.

I get that there are 52 terms because it is for the second year (52 days). I also get that it increases by 11 each time, because the commission in the second year is £11 per week.

HOwever, I don't get why after the final week and final term (where it says 52), why there is a "x 11" after that, and I don't get why it is multiplied by 11.

Please can someone explain to me why the 52 is multiplied by 11?

Any help would be greatly appreciated, Thanks!

(edited 7 years ago)

Reply 1

ghostwalker

Original post by blobbybill

Please can someone explain to me why the 52 is multiplied by 11?

Any help would be greatly appreciated, Thanks!

Is this the line following "commission for year 1 policies +...". If so,

The numbers in brackets are (11+22+33+....
i.e. (1x11 + 2x11 + 3x11 +... + 52x11)

They put it as 52x11, rather than work out the actual value of 572.

Reply 2

blobbybill

Original post by ghostwalker

Ah ok, so if they put it as 572, that would be the final term?

Also, in the equation of Sn = n/2 [2a + (n-1)d], the solutions show n to be n=52. How would you know whether n would be 52 or 572 when substituting it into the equation? I can see its 52 now, but if it came up in an exam, i wouldnt know whether to use 52 (because 52 weeks in year), or 572 (because its the value of the final term)?

Thanks!

Reply 3

ghostwalker

Original post by blobbybill

Ah ok, so if they put it as 572, that would be the final term?

Yes.

Also, in the equation of Sn = n/2 [2a + (n-1)d], the solutions show n to be n=52. How would you know whether n would be 52 or 572 when substituting it into the equation? I can see its 52 now, but if it came up in an exam, i wouldnt know whether to use 52 (because 52 weeks in year), or 572 (because its the value of the final term)?

Thanks!

In the formula for Sn, "n" is the number of terms in the arithmetic progression, hence 52, not 572.