Question

What is the 214 term in the sequence 7,10,13,16?

Answer 1

We can figure this out using the explicit formula.

$f(n)=f(1)+d(n-1)$

n represents the term we are looking for.
f(1) represents the first term in the sequence, which in this case, is 7.
d represents the common difference, which in this case, is +3.

f(n) = 7 + 3(n - 1)
f(n) = 7 + 3n - 3
f(n) = 4 + 3n

Now, we can input 214 for n and solve.

f(214) = 4 + 3(214)
f(214) = 4 + 642
f(214) = 646

The 214th term in this sequence is 646.