Asequence is defined recursively by the formula f(n + 1) = –2f(n). the first term of the sequence is –1.5. what is the next term in the sequence? –3.5 –3 0.5 3

  3

Step-by-step explanation:

Put the given numbers in the formula and do the arithmetic.

  f(2) = -2·f(1) = -2·(-1.5) = 3

The next term of the sequence is 3.

3.

Step-by-step explanation:

Given : A sequence is defined recursively by the formula

The first term of the sequence is -1.5.

i.e.

To find the next term , we put n=1 in the given expression, we get

Hence, the next term in the sequence is 3.

This is because the given expression factors to (x+4)(x+4), which condenses to (x+4)^2.

To factor, think of two numbers that A) multiply to 16, and B) add to 8. Those values would be 4 and 4

4+4 = 8

4*4 = 16

So that's how we end up with (x+4)(x+4). You can use the FOIL rule to expand that out and get x^2+8x+16 again to help verify you have the correct factorization.