Question

a1=10an=an-1+4 ??????? help pls

Answer 1

I assume you're asked to solve for $a_n$, or find an explicit formula for the n-th term in the sequence.

The sequence is recursively defined by

$\begin{cases} a_1 = 10 \\ a_n = a_{n-1} + 4 & \text{for } n \ge 1 \end{cases}$

By this definition,

$a_{n-1} = a_{n-2} + 4$

so that by substitution,

$a_n = (a_{n-2} + 4) + 4 = a_{n-2} + 2\times4$

and we can repeat this process to find

$a_n = a_{n-3} + 3\times4$

$a_n = a_{n-4} + 4\times4$

and so on, down to

$a_n = a_1 + (n-1)\times4$

Then given the first term $a_1=10$, we have

$a_n = 10 + 4(n-1) \implies \boxed{a_n = 4n + 6}$