Question

The first two terms of an arithmetic sequence are 7 and 4. Find the 7th term.

Answer 1

EXPLANATION

If the first two terms of an arithmetic sequence are 7 and 4, then we know that an arithmetic sequence has a constant difference d and is defined by

$a_n=a_1+(n+1)d$

Check wheter the difference is constant:

Compute the differences of all the adjacent terms:

$d=a_{n+1}-a_n$

Replacing terms:

4-7 = -3

The difference between all of the adjacent terms is the same and equal to

d = -3

The first element of the sequence is

$a_1=7$$a_n=a_1+(n+1)d$

Therefore, the nth term is computed by

d= -3

$a_n=7+\text{ (n-1)}\cdot(-3)$

Refine

d= -3 ,

$a_n=-3n+10$

Now, replacing n=7

$a_7=-3\cdot7+10\text{ = -11}$

So, the answer is -11.