5th term; if a3 = 10 and a7 = 26

Since the 7th term=26

And the 3rd term =10

7 - 3 =4 the difference between the 2 terms

26 - 10 =16 the difference between their values, therefore:

16 / 4 = 4 common difference

5th term=3rd + (2 x 4)

             =10 + 8

             = 18

If it's an arithmetic sequence:                (d  is the common difference)

     a₃  =  10

     a₄  =  a₃ + d  =  10 + d

     a₅  =  a₄ + d  =  (10 + d) + d  =  10 + 2d

     a₆  =  a₅ + d  =  (10 + 2d) + d  =  10 + 3d

     a₇  =  a₆ + d  =  (10 + 3d) + d  =  10 + 4d

 

Since  a₇  =  26   --->   26  =  10 + 4d

                                       16  =  4d

                                         4  =  d

 

Since  a₅  =  10 + 2d   --->   a₅  =  10 + 2(4)  =  10 + 8  =  18