Question 1178154


{{{88}}},{{{83}}}, {{{78}}}, {{{73}}},...

1st term {{{a[1]=88}}}
2nd term {{{a[2]=83=88-5}}}
3rd term {{{a[3]=78=83-5}}}

=> common difference is {{{d=-5}}} 


i) Classify each as arithmetic, geometric, and/or none of these. 

=> common difference is {{{d=5}}}, so you have an arithmetic sequence

{{{n}}}th term formula will be:

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

{{{a[n]=88-5(n-1)}}}
 


ii)  Find the {{{28}}}th term.  

{{{a[28]=88-5(28-1)}}}

{{{a[28]=88-5(27)}}}

{{{a[28]=88-135}}}

{{{a[28]=-47}}}


iii)  Find the sum of the first {{{7 }}}terms, call it {{{S7}}} . 

first find {{{5}}}th, {{{6}}}th, and {{{7}}}th term

{{{a[5]=88-5(5-1)=88-5*4=88-20=68}}}

{{{a[6]=88-5(6-1)=88-5*5=88-25=63}}}

{{{a[7]=88-5(7-1)=88-5*56=88-30=58}}}


{{{88}}},{{{83}}}, {{{78}}}, {{{73}}},{{{68}}},{{{63}}},{{{58}}}


the sum is {{{S[7]=88+83+78+73+68+63+58=511}}}