Explain whether the following statement is true or false: $100 a year for 10 years is an annuity; but $100 in Year 1, $200 in Year 2, and $400 in Years 3 through 10 does not constitute an annuity. However, the second series contains an annuity

An annuity is a series of \textit{equal}equal payments paid at specific intervals of time for a specified period of time.  The first statement is true since it is a series of \textit{equal}equal payments ($100) at specific intervals of time (per year) for a specified period of time (10 years).  The second statement is true since the payments are indeed not equal, although paid at specific intervals of time for a specific period of time. The second series did contain an annuity \textit{within}within its series of payments: $400 in years 3 through 10. But do take note that the \textit{entire}entire series itself or the series taken as a whole does not constitute an annuity.