Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. 9, 10, 11, 12, ...
Accepted Solution
A:
Answer:[tex]T_n= 9+(n-1)[/tex]Step-by-step explanation:The Given sequence is 9, 10, 11, 12We need to find the expression to describe the sequence.Let [tex]T_n[/tex] be the [tex]n^{th}[/tex] term of the sequence.Let n represent the position of the term.Let a be the first term in the sequence.and d be the common difference between the sequenceHence the expression to find the above sequence is given below;[tex]T_n= a+(n-1)d[/tex]when n=1 d= 1 a = 9[tex]T_1 = 9+(1-1)1 = 9 + 0 = 9[/tex]when n=2 d= 1 a = 9[tex]T_2 = 9+(2-1)1 = 9 + 1 = 10[/tex]when n=3 d= 1 a = 9[tex]T_3 = 9+(3-1)1 = 9 + 2 = 11[/tex]when n=3 d= 1 a = 9[tex]T_4 = 9+(4-1)1 = 9 + 3 = 12[/tex]Hence the expression is [tex]T_n= 9+(n-1)[/tex]