Question 1138280


find the missing term between {{{-5}}} and {{{-2}}}

if given terms of arithmetic sequence

{{{-5}}} ,{{{a[2]}}},{{{-2}}}

first we need to find common difference {{{d}}}:

{{{a[1]=-5}}}
{{{a[3]=-2}}}

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

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

2nd term is:

{{{a[2]=-5+(2-1)d}}}
{{{a[2]=-5+d}}}........eq.1

3rd term is:

{{{a[3]=-5+(3-1)d}}}
{{{-2=-5+2d}}}
{{{-2+5=2d}}}
{{{2d=3}}}
{{{d=3/2}}}=>common difference


and, nth term formula is:

{{{a[n]=-5+(n-1)(3/2)}}}

then, 2nd (eq.1) term is:

{{{a[2]=-5+3/2= -7/2=-3.5}}}


check all terms:

{{{a[n]=-5+(n-1)(3/2)}}}
{{{n=1}}}
{{{a[1]=-5+(1-1)(3/2)=-5+0(3/2)=-5}}}

{{{n=2}}}
{{{a[2]=-5+(2-1)(3/2)=-5+(3/2)=-7/2=-3.5}}}

{{{n=3}}}
{{{a[3]=-5+(3-1)d=-5+2*(3/2)=-2}}}