Question

For the pattern 68, ___, 54 to be an arithmetic sequence, the number that can be filled in the blank is .

Answer 1

Let the arithmetic sequence is $68,x,54.$
For an arithmetic sequence, we know that the next term is formed by adding a constant value to its preceding term.
Let's say the constant term is $d.$
$\therefore x=68+d..\left(a\right)$
Again, $54=x+d...\left(b\right)$

Now solve these simultaneous equations.
From (b) $d=54-x$
Substitute $d$ in (a)
$x=68+54-x$
$\Rightarrow 2x=122$
$\Rightarrow x=61$

The sequence is $68,61,54.$