Question

a1 = 10 and an =an -1 +2

Answer 1

I assume you're asking to solve for the n-th term in the sequence, $a_n$.

From the given recursive rule,

$a_n = a_{n-1} + 2 \implies a_{n-1} = a_{n-2} + 2$

and by substitution,

$\implies a_n = a_{n-2} + 2\times2$

Similarly,

$a_n = a_{n-1} + 2 \implies a_{n-2} = a_{n-3} + 2$

$\implies a_n = a_{n-3} + 3\times2$

The pattern continues, so that we can write the n-th term in terms of the 1st one:

$a_n = a_1 + (n-1)\times2 \implies a_n = 10 + 2(n-1) = \boxed{2n+8}$

So the first few terms of the sequence are

{10, 12, 14, 16, 18, 20, …}