To determine if a general term represents a sequence, simply try out some values of \(n\). If we put \(n=1\) into the first options, we only find that the second option gives the correct first term, i.e. \(5(1)+5=10\).

To determine if a general term represents a sequence, simply try out some values of \(n\). If we put \(n=1\) into the first options, we only find that the second option gives the correct first term, i.e. \(5(1)+7=12\).

To determine if a general term represents a sequence, simply try out some values of \(n\). If we put \(n=1\) into the first options, we only find that the fourth option gives the correct first term, i.e. \(1^2+2(1)+4=7\).

For a linear sequence, the difference between terms is constant.

For a linear sequence, the difference between terms is constant. In this case, that difference is \(5-3=2\). Therefore, the next term in the sequence will be \(2\) more than the previous term, i.e. \(5+2=7\).

For a quadratic sequence, the "difference of the differences" is constant. In this case, this "difference of the differences" is \(26-21=5\). Therefore, the difference between the next two terms will be \(5\) more than the previous two terms, i.e. it will be \(26+5=31\).

Any kind of sequence with an \(an^2\) term is quadratic.

This is a first order difference equations​ as it is of the form \(T_{n+1} = aT_{n} + b\).

This is a second-order inhomogeneous difference equations​ as it is of the form \(aT_{n+2} + bT_{n+1}+cT_{n} = d\).

This is a second-order homogeneous difference equations​ as it is of the form \(aT_{n+2} + bT_{n+1}+cT_{n} = 0\).

This is a second-order inhomogeneous difference equations​ as it is of the form \(aT_{n+2} + bT_{n+1}+cT_{n} = d\).

This is a first order difference equations​ as it is of the form \(T_{n+1} = aT_{n} + b\).