Question 650861
1.

If we start with an odd number and each number in the sequence is {{{2}}} more than the previous number then we will get consecutive odd integers.

if first one is {{{x}}}, second one will be {{{x+2}}}, and third one will be {{{x+4}}}

the sum is: {{{x+(x+2)+(x+4)=-3}}}

{{{x+(x+2)+(x+4)=-3}}}...solve for {{{x}}}

{{{3x+6=-3}}}

{{{3x=-3-6}}}

{{{3x=-9}}}

{{{x=-9/3}}}

{{{highlight(x=-3)}}}....first number

second one will be {{{x+2}}}...->...{{{-3+2}}} ...->...{{{highlight(-1)}}}

third one will be {{{x+4}}}...->...{{{-3+4}}} ...->...{{{highlight(1)}}}


so, the numbers are:{{{highlight(-3)}}},{{{highlight(-1)}}}, and {{{highlight(1)}}}; as you can see, the greatest one is {{{highlight(1)}}}


2.

The sum of three {{{consecutive}}} integers is {{{0}}}. What is the smallest integer?

If we start with an integer, each next {{{consecutive}}}integer in the sequence is {{{1}}} more than the previous one

if first one is {{{x}}}, second one will be {{{x+1}}}, and third one will be {{{x+2}}}

the sum is: {{{x+(x+1)+(x+2)=0}}}...solve for {{{x}}}

{{{3x+3=0}}}

{{{3x=-3}}}

{{{x=-3/3}}}

{{{highlight(x=-1)}}}

second one will be {{{x+1}}}...->...{{{-1+1}}} ...->...{{{highlight(0)}}}

third one will be {{{x+2}}}...->...{{{-1+2}}} ...->...{{{highlight(1)}}}


so, the numbers are:{{{highlight(-1)}}},{{{highlight(0)}}}, and {{{highlight(1)}}}; as you can see, the smallest integer is {{{highlight(-1)}}}