`a_4 = 16, a_10 = 46` Write the first 5 terms of the arithmetic sequence.

Expert Answers
lemjay eNotes educator| Certified Educator

`a_4=16 `  

`a_10=46`

To determine the first five terms of this arithmetic sequence, consider its nth term formula which is:

`a_n=a_1+(n-1)d`

To apply this, plug-in the given nth terms.

Plugging in a_4=16, the formula becomes:

`16=a_1 + (4-1)d`

`16=a_1+3d `          (Let this be EQ1.)

Also, substituting a_10=46, the formula becomes:

`46=a_1+(10-1)d`

`46=a_1+9d `          (Let this be EQ2.)

Then, use these two equations to solve for the values of a_1 and d. To do so, isolate a_1 in the first equation.

`16=a_1+3d`

`16-3d=a_1`

Plug-in this to the second equation.

`46=a_1+9d`

`46=16-3d+9d`

`46=16+6d`

`30=6d`

`5=d`

Then, solve for a_1. To do so, plug-in d=5 to the first equation.

`16=a_1 + 3d`

`16=a_1+3(5)`

`16=a_1+15`

`1=a_1`

Then, plug-in these two values a_1=1 and d=5 to the formula of nth terms of arithmetic sequence.

`a_n=a_1+(n-1)d`

`a_n=1+(n-1)(5)`

`a_n=1+5n-5`

`a_n=5n-4`

Now that the formula of a_n is known,  use this to solve for the values of a_2, a_3 and a_5.  (Take note that the values of a_1 and a_4 are already known.)

1st term: `a_1=1`

2nd term: `a_2=5(2)-4=6`

3rd term: `a_3=5(3)-4=11`

4th term: `a_4=16`

5th term: `a_5=5(5)-4=21`

Therefore, the first five terms of the arithmetic sequence are {1, 6, 11, 16, 21,...}.