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r-ruslan [8.4K]
3 years ago
9

Write the sum using summation notation, assuming the suggested pattern continues. -3+6+15+24+...+132

Mathematics
1 answer:
balandron [24]3 years ago
7 0

Answer:

Option (4)

Step-by-step explanation:

Given sequence is,

-3 + 6 + 15 + 24 + ........+ 132

Difference in 1st and 2nd term = 6 - (-3)

                                                   = 9

Difference in 2nd and 3rd term = 15 - 6

                                                    = 9

There is a common difference of 9 in each successive term.

Therefore, it's an arithmetic sequence.

Let the nth term of this sequence is (a + bn).

For the first term → n = 0,

a = -3

For second term → n = 1

-3 + b(1) = 6

b = 6 + 3

b = 9

Therefore, nth term of the sequence will be,

T_n = -3 + 9n

For nth term = 132

-3 + 9n = 132

9n = 135

n = \frac{135}{9}

n = 15

Sum of 15 terms can be represented by the expression;

\sum_{n=0}^{15}(-3+9n)

Option (4) is the answer.

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nikitadnepr [17]

This question is incomplete

Complete Question

An arts academy requires there to be 6 teachers for every 132 students and 4 tutors for every 44 students. How many students does the academy have per​ teacher? Per​ tutor? How many tutors does the academy need if it has 132 students​?

Answer:

a)How many students does the academy have per​ teacher?

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b) Per​ tutor?

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a)How many students does the academy have per​ teacher?

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4 × x = 1 × 44

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c) How many tutors does the academy need if it has 132 students​?

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Cross Multiply

44 × x = 132 × 4

44x = 132 × 4

x = 132 × 4/44

x = 12 tutors

The academy needs 12 tutors if they have 132 students.

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