sequence

Sum of arithmetic sequence

 Sum₃₂ =  n/2 ( 2a₁ + (n-1)d)

             = 32/2 (2a₁  + (32-1)d)

1448    = 16 (2a₁ + 31d)

 

 

5th term = 18 = a₁ + 4d    so   a₁ = 18- 4d     use this value of a₁ in the red equation above to calculate 'd'

 

then  ninth term will be:    5th term + 4d  = 18 + 4(d)