Question

1. In an arithmetic sequence, if a4 = 18 and a10 = 30, determine a1, d, and an.

Answer 1

In an arithmetic sequence, if a4 = 18 and a10 = 30, determine a1, d, and an.

Then write the first four terms of the sequence.

Use the formula  L = A + (N-1)D, where L represents the nth term.

Then, based upon the given info,  

18 = A + (4-1)D and   30 = A + (10-1)D.  
The first equation boils down to 18 = A + 3D, so that A = 18 - 3D.  Subst. 18-3D for A in the second equation:  30 = 18-3D + 9D.  Then 12=6D and D = 2.

Use A = 18 - 3D to determine the value of A.  Recall that D=2.

Then A = 18 - 3(2), or A = 18-6, or A = 12.

Then L = A + (N-1)D becomes   L = 12 + (N-1)(2).

First term is 12.  Next is 14; next is 16; last is 18.