Use the given information about the arithmetic sequence to f

Use the given information about the arithmetic sequence to find a formula for a_n

Use the given information about the arithmetic sequence to find a formula for a_n a_3 = 7, a_8 = 32 a_10 = 103, a_16 = 85

Solution

a₃=7

a_n=a₁+(n-1)d

Therefore

a₃=a₁+2d=7

a₈=a₁+7d=32

Subtracting both equations

5d=25

d=5

a₁+10=7

a₁=-3

a_n=-3+(n-1)5 =5n -8