Question

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

Answer 1

`\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}`