Guerrero Carter
11/27/2023 · Elementary School
QUESTION 4 The quadratic pattern: \( 3 ; x ; 10 ; y ; 21 ; \ldots \) has a constant second difference of 1. Calculate the values of \( x \) and \( y \). 4.1 Determine \( T_{n} \) the general term of the sequence. 4.2 prove algebraically that the sum of any two consecutive terms is a 4.3 perfect square.
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x = 6, y = 15, general term: \( T_n = \frac{1}{2}n^2 + \frac{3}{2}n + 1 \), sum of consecutive terms is a perfect square.
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