



 
Hi Vicki, A geometric sequence has the form \[a, ar, ar^2, ar^3, ...\] for some numbers $a$ and $r.$ The fact that "The sum of the first three terms of a geometric sequence of positive integers is equal to seven times the first term" tells you that \[a + ar + ar^2 = 7a.\] You can divide both sides of this equation by $a$ to obtain \[1 + r + r^2 = 7.\] Solve this quadratic for $r.$ There are two solution but you need the one that is positive. Now take the second fact "and the sum of the first four terms is fortyfive" and use it to write an equation. Substitute the value you found for $r$ and solve for $a.$ I hope this helps,  


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