Solve the problem 1. Which term of the arithmetic sequence 2,5,8,...is 110?2. The first term of an arithmetic sequence is 5, and the common difference is 4, is 2917 term of this sequence? if so, which
Answer (1)
Problem 1:Identify the patternThe arithmetic sequence increases by 3 each time (5 - 2 = 3, 8 - 5 = 3). This is the common difference (d).FormulaThe nth term of an arithmetic sequence is given by the formula: [tex]$\sf{a_n = a_1 + (n-1)d}$[/tex], where [tex]$\sf{a_n}$[/tex] is the nth term, [tex]$\sf{a_1}$[/tex] is the first term, n is the term number, and d is the common difference.Apply the formulaWe know [tex]$\sf{a_n}$[/tex] = 110, [tex]$\sf{a_1}$[/tex] = 2, and d = 3. We need to solve for n: 110 = 2 + (n - 1)3108 = (n - 1)336 = n - 1n = 37Final answer: 110 is the 37th term of the arithmetic sequence.Problem 2:Identify the knowns[tex]$\sf{a_1}$[/tex] = 5, d = 4. We want to know if 2917 is a term in the sequence and, if so, which term.Apply the formula (again)We'll use the same formula, but this time we'll solve for 'n' given [tex]$\sf{a_n}$[/tex] = 2917: 2917 = 5 + (n - 1)42912 = (n - 1)4728 = n - 1n = 729Final answer:Yes, 2917 is a term in this sequence. It is the 729th term.
