Pierce Vaughan
05/10/2023 · Primary School
The sequence \( 3 ; x ; 10 ; y ; 21 ; \ldots \) has a quadratic pattern. a Calculate the values of \( x \) and \( y \). b Determine a formula for the nth term of the sequence. c Hence, prove algebraically that the sum of any two consecutive terms is a perfect square.
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a) \( x = 10 \) and \( y = 37 \).
b) The formula for the nth term is \( f(n) = \frac{11}{5}n^2 + \frac{2}{5}n + \frac{2}{5} \).
c) The sum of any two consecutive terms is a perfect square.
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