MCR3U1 - Sequences Quiz Completion Complete each statement. 1. The expression t_(n)=2n^2+1 is considered the __ formula of a sequence. 2.Find the first 5 terms in the sequence that has the general term t_(n)=2n^2+1 __ , __ __ __ , __ The formula for the general term of a sequence where the value of the first term and a defining equation based on the previous term are given is called the __ formula. The sequence 1, 1,23,5,8,13,21 __ is referred to as the __ sequence. The coefficients in the expansion of (x+y)^7 can be found using row __ of Pascal's triangle.

## Step1: Identify the type of formula<br />### The expression $t_{n}=2n^{2}+1$ is a direct formula for finding the terms of a sequence based on the position $n$. This is known as the "general" formula.<br />## Step2: Calculate the first 5 terms<br />### To find the first 5 terms, substitute $n = 1, 2, 3, 4, 5$ into the general formula $t_{n}=2n^{2}+1$.<br />For $n=1$: $t_{1} = 2(1)^{2} + 1 = 3$<br />For $n=2$: $t_{2} = 2(2)^{2} + 1 = 9$<br />For $n=3$: $t_{3} = 2(3)^{2} + 1 = 19$<br />For $n=4$: $t_{4} = 2(4)^{2} + 1 = 33$<br />For $n=5$: $t_{5} = 2(5)^{2} + 1 = 51$<br />The first 5 terms are $3, 9, 19, 33, 51$.<br />## Step3: Identify the recursive formula<br />### A formula that defines each term based on the previous term(s) is called a "recursive" formula.<br />## Step4: Identify the Fibonacci sequence<br />### The sequence $1, 1, 2, 3, 5, 8, 13, 21, \ldots$ is known as the "Fibonacci" sequence.<br />## Step5: Find the row in Pascal's triangle<br />### The coefficients in the expansion of $(x+y)^{7}$ correspond to row 7 of Pascal's triangle.