Your method is completely correct. The first term will be 6 and each subsequent term can be obtained by adding 6 to the previous one, meaning the common difference is 6. The number of terms is given by the highest number that is divisible by 6 and dividing it by 6; that is 996/6 = 166
Then we simply apply the formula for arithmetic sequence sum:
S = n/2 [2a₁ + (n - 1)d]
S = 166/2 [ 2(6) + (166 - 1)6]
S = 83,166

8 0

3 years ago

A high-altitude spherical weather balloon expands as it rises, due to the drop in atmospheric pressure. Suppose that the radius

lord [1]

The increase of the radius is a linear increase since we have the constant rate of 0.07 inches per second

The equation for a linear growth/decay is given by the form $y=mx+c$ where $m$ is the rate of increase and $c$ is the value of $y$ when $x=0$

We have
$m = 0.07$
$c=36$ when $t=0$

So the equation is $r=0.07t+36$

The length of the radius when $t=400$ seconds is
$r=0.07(400)+36$
$r=64$ inches

7 0

2 years ago