# Math Help - find next term

1. ## find next term

Given the sequence, what is the value of a?
. . .3, 10, 31, a , 283, . .

2. Hello, JoDan!

Given the sequence, what is the value of a?
. . $3,\:10,\:31,\:a,\;283, \cdots$

There isn't much to work with . . .

The differences are: . $3\underbrace{\qquad}_7 10\underbrace{\qquad}_{21}31 \underbrace{\qquad}_? a \underbrace{\qquad }_? 283$

I conjectured that the differences are: . $7,\;7\!\cdot\!3,\;7\!\cdot\!3^2,\;7\!\cdot\!3^3$

. . and it worked!

. . . . . $3\underbrace{\qquad}_7 10\underbrace{\qquad}_{21}31 \underbrace{\qquad}_{63} {\color{blue}94} \underbrace{\qquad }_{189} 283$