9231 FP1 · Notes & worked examples
Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.
Recall
Maths4U Original · Short practice
Define \(S_n=\sum_{r=1}^n(12r+11)\) for positive integers n.
Find the sum from \(\displaystyle r=1\) to \(\displaystyle r=13\) of 12r+11.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
Define \(S_n=\sum_{r=1}^n(13r+12)\) for positive integers n.
Find the sum from \(\displaystyle r=1\) to \(\displaystyle r=14\) of 13r+12.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Method
Maths4U Original · Short practice
Define \(S_n=\sum_{r=1}^n(13r+12)\) for positive integers n.
Find the term added when extending \(\displaystyle S_{14}\) to \(\displaystyle S_{15}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
Define \(S_n=\sum_{r=1}^n(14r+13)\) for positive integers n.
Find the term added when extending \(\displaystyle S_{15}\) to \(\displaystyle S_{16}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Apply
Maths4U Original · Short practice
Work with the integer powers \(4^n-2^n\).
Find the quotient at \(\displaystyle n=4\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
Work with the integer powers \(6^n-3^n\).
Find the quotient at \(\displaystyle n=5\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Check understanding
Maths4U Original · Short practice
\(u_1=14,\ u_{n+1}=3u_n+15\) for \(\displaystyle n\ge 1\).
Find \(\displaystyle u_{6}-u_{5}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
\(u_1=15,\ u_{n+1}=4u_n+16\) for \(\displaystyle n\ge 1\).
Find \(\displaystyle u_{7}-u_{6}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.