In an arithmetic​ sequence, the nth term an is given by the formula An=a1+(n−1)d​, where a1is the first term and d is the common difference.​ Similarly, in a geometric​ sequence, the nth term is given by an=a1•rn−1.Use these formulas to determine the indicated term in the given sequence.The 19th term of 19​,42​,65​,88​,...

Accepted Solution

Answer: 433Step-by-step explanation:The given sequence : 19​,42​,65​,88​,...We can see that the terms ha common difference as :-[tex]42-19=23\\65-42=23\\88-65=23[/tex]Thus, its an Arithmetic progression with common difference (d)=23The formula to find the nth term is :-[tex]a_n=a_1+(n-1)d[/tex]Now, the 19th term of the given sequence :-[tex]a_{19}=19+(19-1)(23)\\\\=19+(18)(23)\\\\=19+414=433[/tex]Hence, the 19th term of 19​,42​,65​,88​,... is 433.