Given the sequence, what is the value of a?
. . .3, 10, 31, a , 283, . .
Hello, JoDan!
Given the sequence, what is the value of a?
. . $\displaystyle 3,\:10,\:31,\:a,\;283, \cdots$
There isn't much to work with . . .
The differences are: .$\displaystyle 3\underbrace{\qquad}_7 10\underbrace{\qquad}_{21}31 \underbrace{\qquad}_? a \underbrace{\qquad }_? 283 $
I conjectured that the differences are: .$\displaystyle 7,\;7\!\cdot\!3,\;7\!\cdot\!3^2,\;7\!\cdot\!3^3$
. . and it worked!
. . . . . $\displaystyle 3\underbrace{\qquad}_7 10\underbrace{\qquad}_{21}31 \underbrace{\qquad}_{63} {\color{blue}94} \underbrace{\qquad }_{189} 283 $