



 
Hi Moti, If the first term of the arithmetic sequence is $a_1$ and the common difference id $d$ what is the 20th term? What is the 58th term? The problem says the $a_1$ is also some term in a geometric sequence, lets call it $b.$ Suppose also that the common ratio of the geometric sequence is $r.$ In a geometric sequence each term after the first is $r$ times the previous term so the next term after $b$ is $b \times r$ and the term after that is $b \times r \times r.$ These three terms are the same as the three terms in the arithmetic sequence mentioned above. This gives toy three equations. Solve them for $r.$ Write back if you need more assistance, 



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