How many multiples of 9 are there between 100 and 2,000?

hint: an = a1 + d (n − 1), where a1 is the first term and d is the common difference.

211

212

196

210

First Option

The number of multiples of 9 is 211

Step-by-step explanation:

Note that the first multiplo of 9 between 100 and 2000 is number 108. The last multiple of 9 is 1998.

If we use the arithmetic sequence to perform the calculation

So the first term is:

The last term is

The common difference is

Thus

We solve the equation for n and obtain the number of multiples of 9.

b

step-by-step explanation:

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.