C2 - Sequences and Series

Hi,

I'm stuck on these questions and can't seem to get the right answers, so was hoping someone could help, showing their method for working it out:

1) The sum of the first n terms of a certain sequence is 3n²+10n for all values of n.

Find the nth term by calculating S(n)-S(n-1) (the bits in brackets are written below S)

The answer is 6n+7

2) A child wishes to build up a triangular pile of toy bricks so as to have 1 brick in the top row, 2 in the second, 3 in the third and so on. If he has 100 bricks, how many rows can he complete and how many bricks will he have left over?

Answer: 13 rows, 9 left over

Thanks very much for your help

Reply 1

Libertine

sweet_gurl

Just insert (n-1) into formula for sum of terms to get S(n-1)

3n²+10n - (3(n-1)²+10(n-1))=3n²+10n-3n²+6n-3-10n+10
= 6n + 7

Reply 2

Libertine

sweet_gurl

2) A child wishes to build up a triangular pile of toy bricks so as to have 1 brick in the top row, 2 in the second, 3 in the third and so on. If he has 100 bricks, how many rows can he complete and how many bricks will he have left over?

Answer: 13 rows, 9 left over

Use formula for sum of an arithmetic sequence and make it less than or equal to 100. So:
S(n) = n/2(n+1)<100
=n²/2 + n <100
=n² + 2n <200
=n(n+2) <200
Lowest integer numbers 2 apart that multiply to give less than 200 are 13 and 15

Therefore the maximum 'n' can be is 13. If n = 13:
No. of bricks used = S(n)
=13/2.(13+1)
=91 bricks used
100-91=9
So 9 left over