So I just completed my IGCSE Edexcel maths paper 2H, and the last question go to me a lot...

Question

So it was: "The sum of the first 43 numbers in an arithmetic series is 4 x(times) the sum of the first 30. Find the sum of the first 30?". I started by using the sum of the nth term equation like this: 4 x (equation) = (equation). It took me a while using this method and ultimately I ran out of space and time :( I was wondering if this method would have got me close to the answer, (meaning i got method marks) or if it is completely incorrect maybe you could help me with providing an answer?

I am from the UK so the zip code i entered is a random one, sorry.

Answer 1

Try an easier problem to see the method better

S2 = sum of 1st 2 integers = 1+2 = 3

S5 = sum of 1st 5 integers = 1+2+3+4+5 = 15

15 = 5x3

S5=5S2

Use Gaus's formula n(n+1)/2 = Sn

S2 = 2(3)/2 = 3

S5= 5(6)/2 = 15

S2 = 1 + (1+ d) = 2+d, where d= the common difference

S5 = 1 + (1+d) + (1+2d) + (1+3d) + (1+4d)= 5+10d

5+10d + 5(2+d) = 10+5d

5d =5

d = 1

the arithmetic sequence is 1,2,3,4,5,

Now do the same for S43 and S30

S43 = 43+903d

S30 = 30+465d

S43=4S30

43+903d = 4(30+465d)

1860d-903d = 43-120

d=-77/957= about -0.08046

the arithmetic sequence is

1, 1-77/957, 1 - 154/957, ... ...., 1-(42)(77)/957 for first 43 terms.

You can also multiply each term by a = any constant and S43 will still = 4(S30)

just as 2+4=6

and 2+4+6+ 8+ 10 = 30

with 30=5(6)