Question 1158458


13.

 an Arithmetic Sequence as a rule:

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

{{{a[32]=622 }}}->{{{n=32}}} if {{{d=20}}}

{{{622 = a[1] + 20(32-1)}}}

{{{622 = a[1] + 20(31)}}}

{{{622 = a[1] + 620}}}

{{{ a[1]= 622- 620}}}

{{{ a[1]= 2}}}

 the explicit formula is:

{{{a[n] = 2 + 20(n-1)}}}

the {{{52}}}nd term is:

{{{a[52] = 2 + 20(52-1)}}}

{{{a[52] = 2 + 20(51)}}}

{{{a[52] = 2 + 1020}}}

{{{a[52] = 1022}}}


14.

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

{{{a[18]=-166 }}}->{{{n=18}}} if {{{d=-8}}}

{{{-166= a[1] -8(18-1)}}}

{{{-166= a[1] -8(17)}}}

{{{-166= a[1] -136}}}

{{{136-166= a[1] }}}

{{{a[1] =-30}}}

 the explicit formula is:

{{{a[n] = -30 -8(n-1)}}}


the {{{52}}}nd term is:

{{{a[52] = -30 -8(52-1)}}}

{{{a[52] = -30 -8(51)}}}

{{{a[52] = -30 -408}}}

{{{a[52] =  -438}}}