Question 1115601

to find the {{{19th}}} term of {{{3/8}}}, {{{1/2}}}, {{{5/8}}}  or {{{3/8}}}, {{{4/8}}}, {{{5/8}}}  

first find common difference {{{d}}}

 {{{d=1/2-3/8=4/8-3/8=1/8}}} or

{{{d=5/8 -1/2=5/8-4/8=1/8}}}

so, {{{d=1/8}}}

since first term {{{a[1]=3/8}}}, {{{19th}}} term =>{{{n=19}}}

use formula

{{{a[n]=a[1]+(n-1)d}}}

{{{a[19]=3/8+(19-1)(1/8)}}}

{{{a[19]=3/8+18/8}}}

{{{a[19]=21/8}}}

your sequence is:

{{{3/8}}}, {{{4/8}}}, {{{5/8}}} ,{{{6/8}}},{{{7/8}}},{{{8/8}}},{{{9/8}}},{{{10/8}}},{{{11/8}}},{{{12/8}}},{{{13/8}}},{{{14/8}}},{{{15/8}}},{{{16/8}}},{{{17/8}}},{{{18/8}}},{{{19/8}}},{{{20/8}}},{{{21/8}}},...

or, simplified

{{{3/8}}}, {{{1/2}}}, {{{5/8}}} ,{{{3/4}}},{{{7/8}}},{{{1}}},{{{9/8}}},{{{5/4}}},{{{11/8}}},{{{3/2}}},{{{13/8}}},{{{7/4}}},{{{15/8}}},{{{2}}},{{{17/8}}},{{{9/4}}},{{{19/8}}},{{{5/2}}},{{{21/8}}},...