A sequence {an} is defined recursively, with a1 = -1, and, for n 1, an = an-1 + (-1)n. Find the first five terms of the sequence.
A)
-1, 0, 1, 2, 3
B)
-1, -2, -3, -4, -5
C)
-1, 0, -1, 0, -1
D)
-1, 1, -1, 1, -1

Question

A sequence {an} is defined recursively, with a1 = -1, and, for n > 1, an = an-1 + (-1)n. Find the first five terms of the sequence.
A)
-1, 0, 1, 2, 3	
B)
-1, -2, -3, -4, -5	
C)
-1, 0, -1, 0, -1	
D)
-1, 1, -1, 1, -1

johnweldon1993 · Answer

$\large a_1 = -1$ and for $\large n>1$ $\large a_n = a_{n-1} + (-1)^n$

Like that?

johnweldon1993 · Answer

I'm just seeing if I wrote it correctly as you have on your paper?

anonymous · Answer

yeah thats right

johnweldon1993 · Answer

Okay

So we know the first term is -1...we are given that...so $\large a_1 = -1$

Now for $\large a_2$ since we are now > 1 ...we use that equation

$$\large a_n = a_{n-1} + -1^n$$

So for n= 2 *the second term

$$\large a_2 = a_{2-1} + -1^2$$
$$\large a_2 = a_1 + -1^2$$

We know $\large a_1$ = -1 so we can replace that

$$\large a_2 = -1 + -1^2$$

What is -1^2? -1 * -1 = 1 right? so

$$\large a_2 = -1 + 1 = ?$$