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in an arithmetic sequence, the 5th term is equal to 75 and the 7th term is equal to 111 write an expression for the nth term of the sequence

1 Answer

4 votes

Answer:


\bold{\underline{a_n=18n-15}}

Explanation:


a_n=a_1+d(n-1)\\\\a_5=a_1+d\cdot4\\\\a_7=a_1+d\cdot6\\\\a_7-a_5=a_1+6d-(a_1+4d)=2d\\\\111-75=2d\\\\2d=36\\\\d=18\\\\\\a_1+18\cdot4=75\\\\a_1=75-72=3\\\\\\a_n=3+18(n-1)=3+18n-18\\\\\underline{a_n=18n-15}

User Gilad Gat
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