Question

what is the next number in this sequence: 2, 6, 10, 14?
select one:
a. 20
b. 18
c. 17
d. 16

a rectangle has an area 40 and a perimeter of 28, what is its length?
select one:
a. 20
b. 4
c. 8
d. 10

Explanation:

Step1: Find sequence common difference

$6-2=4$, $10-6=4$, $14-10=4$

Step2: Calculate next sequence term

$14+4=18$

Step3: Set up rectangle equations

Let $l$ = length, $w$ = width.
Perimeter: $2(l+w)=28 \implies l+w=14$
Area: $l \times w=40$

Step4: Solve for length

From $l+w=14$, $w=14-l$. Substitute into area:
$l(14-l)=40 \implies 14l-l^2=40 \implies l^2-14l+40=0$
Factor: $(l-10)(l-4)=0$. Length is the longer side, so $l=10$.

Answer:

1. b. 18
2. d. 10