212 Calculate the \( 35^{\text {th }} \) term of the quadratic number pattern.

To find the \( 35^{\text{th}} \) term of a quadratic number pattern, we often assume the general form for the \( n^{\text{th}} \) term is \( a_n = An^2 + Bn + C \). To determine the coefficients, we usually need a few initial terms of the sequence. Once you have the coefficients, plug \( n = 35 \) into the equation. For example, if you find that \( A = 2 \), \( B = 3 \), and \( C = 1 \), the formula would be \( a_n = 2n^2 + 3n + 1 \). So for \( n = 35 \), calculate \( a_{35} = 2(35^2) + 3(35) + 1 \), which will yield the \( 35^{\text{th}} \) term of the sequence. Another fun fact: Quadratic sequences can often be identified by their second differences being constant. This means that if you write out the sequence and find the differences between terms, if those differences are the same, you’re dealing with a quadratic pattern!