# A sequence is defined by the recursive function f(n+1) = f(n) - 2 . If  f(1) = 10 , what is  f(3 )?

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

5
Oct 11, 2016

$f \left(3\right) = 6.$

#### Explanation:

Given that, $f \left(n + 1\right) = f \left(n\right) - 2 \Rightarrow f \left(n + 1\right) - f \left(n\right) = - 2$

Since, this last eqn. holds good $\forall n \in \mathbb{N}$, it means that the diff.

of any two consecutive terms of the Seq. is a constant $\ne 0.$

Obviously, the Seq. has to be an Arithmetic Seq. with, first term

$f \left(1\right) = 10 ,$ and, the Common Difference $d = - 2.$

Accordingly, the General ${n}^{t h}$ Term $f \left(n\right)$is given by,

$f \left(n\right) = f \left(1\right) + \left(n - 1\right) d = 10 - 2 \left(n - 1\right) = 12 - 2 n .$

Hence, the Reqd. Term $= f \left(3\right) = 12 - 2 \left(3\right) = 6.$

Alternatively,

f(n+1)=f(n)-2, & f(1)=10.

$\text{:., by taking } n = 1 , f \left(2\right) = f \left(1\right) - 2 = 10 - 2 = 8.$

A$F \mathmr{and} n = 2 , f \left(3\right) = f \left(2\right) - 2 = 8 - 2 = 6 ,$ As Before!

Enjoy maths.!

• 14 minutes ago
• 15 minutes ago
• 15 minutes ago
• 16 minutes ago
• 53 seconds ago
• 2 minutes ago
• 2 minutes ago
• 5 minutes ago
• 9 minutes ago
• 14 minutes ago
• 14 minutes ago
• 15 minutes ago
• 15 minutes ago
• 16 minutes ago