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MrRissso [65]
4 years ago
7

manny’s pizza shows declining sales over the last few months. their net profit in hundreds of dollars follows the arithmetic seq

uence 4, 1, −2, −5, …, −56. what is their total profit over this time period?
Mathematics
1 answer:
marshall27 [118]4 years ago
8 0

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

<em>The total profit over this period is -546</em>

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