The largest and smallest of three consecutive terms in an arithmetic sequence differ by 14. Half of the smallest term is added to each term and the sum of the resulting three numbers is 120. What is the value of the original smallest term?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The largest and smallest of three consecutive terms in an arithmetic sequence differ by 14. Half of the smallest term is added to each term and the sum of the resulting three numbers is 120. What is the value of the original smallest term?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
22
The largest and smallest of three consecutive terms in an arithmetic sequence differ by 14. Half of the smallest term is added to each term and the sum of the resulting three numbers is 120. What is the value of the original smallest term?
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