find the 20th term of the sequence 6,11,16,..
Answer (1)
Find the 20th term of the sequence 6, 11, 16,...Here are the steps to figure out the 20th term:This is an arithmetic sequence with a common difference of 5 (11 - 6 = 5, 16 - 11 = 5).Step 1: Find the general formulaThe general formula for the nth term of an arithmetic sequence is:[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 termn is the term numberd is the common differenceStep 2: Plug in the valuesIn this case, we have:[tex]$\sf{a_1 = 6}$[/tex][tex]$\sf{d = 5}$[/tex][tex]$\sf{n = 20}$[/tex]Substituting these values into the formula:[tex]$\sf{a_{20} = 6 + (20-1)5}$[/tex]Step 3: Calculate the 20th term[tex]$\sf{a_{20} = 6 + (19)5}$[/tex][tex]$\sf{a_{20} = 6 + 95}$[/tex][tex]$\sf{a_{20} = 101}$[/tex]Final answer:The 20th term of the sequence is 101.
