Hi Michael,

A geometric sequence has a particular pattern defined by two numbers, a, the first term and r, the common ratio. The pattern is that you start with the first term, a and then if you have any term in the sequence, to get the next term you multiply the term you have by r. Hence you have

First term: a
Second term: a r
Third term: a r r = a r²

In your sequence the sum of the 2nd and 3rd terms is 60 and hence

a r + a r² = 60

Use the fact that the sum of the 3rd and 4th terms is 240 to find a second equation and then solve the equations for a and r.

Penny

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