WAEC 2022 · Paper 1 · Q17

Sequences, series & binomial expansion

If $U_n = kn^2 + pn$ , $U_1 = -1$ , $U_5 = 15$ , find the values of $k$ and $p$ .

Worked solution (try it first)

Put $n = 1$ : $k + p = -1$ .
Put $n = 5$ : $25k + 5p = 15$ .
Divide by 5 to get $5k + p = 3$ .
Subtract the first equation: $4k = 4$ , so $k = 1$ .
Then $p = -1 - k = -2$ .
So $k = 1$ , $p = -2$ , option C.

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