Consider the number sequence: $$ 5 ; 18 ; 37 ; 62 ; 93 ; \ldots $$ 3.1 If the sequence behaves consistently, determine the next TWO terms of the sequence. 3.2 Determine a formula for the $$ n^{ ext {th }} $$ term of the sequence. 3.3 Use your formula to determine which term in the sequence is equal to 1278 . 3.4 Calculate the value of the number in the $$ 15^{ ext {th }} $$ position of the sequence. 3.5 How are the terms, one after the other, calculated in the sequence? 3.6 Calculate the sum of the first four terms.

Question

Consider the number sequence: $$ 5 ; 18 ; 37 ; 62 ; 93 ; \ldots $$ 3.1 If the sequence behaves consistently, determine the next TWO terms of the sequence. 3.2 Determine a formula for the $$ n^{	ext {th }} $$ term of the sequence. 3.3 Use your formula to determine which term in the sequence is equal to 1278 . 3.4 Calculate the value of the number in the $$ 15^{	ext {th }} $$ position of the sequence. 3.5 How are the terms, one after the other, calculated in the sequence? 3.6 Calculate the sum of the first four terms.

UpStudy AI · Accepted Answer

- 3.1 The next two terms are 130 and 173. - 3.2 The formula for the $$ n^{	ext{th}} $$ term is $$ a_n = 3n^2 + 4n - 2 $$. - 3.3 The $$ 20^{	ext{th}} $$ term is equal to 1278. - 3.4 The value in the $$ 15^{	ext{th}} $$ position is 733. - 3.5 The terms are calculated using the quadratic formula $$ a_n = 3n^2 + 4n - 2 $$. - 3.6 The sum of the first four terms is 122.

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