Question

manny’s pizza shows declining sales over the last few months. their net profit in hundreds of dollars follows the arithmetic sequence 4, 1, −2, −5, …, −56. what is their total profit over this time period?

Answer 1

Answer:

The total profit over this period is -546

Step-by-step explanation:

Given

Sequence: 4, 1, −2, −5, …, −56

Required

Determine the total profit

To do this, we simply calculate the sum of terms (Sn)

$S_n = \frac{n}{2}(a + T_n)$

But first, we need to determine the value of n using

$T_n = a + (n - 1)d$

Where:

$T_n = -56$

$a = 4$

$d = 1 -4= -3$

Substitute these values in the above formula, we have:

$-56 = 4 + (n - 1) * -3$

$-56 = 4 -3n +3$

Collect Like Terms

$3n = 56 + 4 + 3$

$3n = 63$

$n = 63/3$

$n = 21$

Recall that:

$S_n = \frac{n}{2}(a + T_n)$

This gives:

$S_n = \frac{21}{2}(4 - 56)$

$S_n = \frac{21}{2}(-52)$

$S_n = 21 * -26$

$S_n = -546$

The total profit over this period is -546