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sladkih [1.3K]
3 years ago
10

The 6th term of an arithmetic progression is 35 and the 13th term is 77. find the 1st term

Mathematics
1 answer:
GenaCL600 [577]3 years ago
8 0

Answer:

5

Step-by-step explanation:

The 6th term of an arithmetic progression is 35 and the 13th term is 77. find the 1st term

We know we have an arithmetic sequence.

a_n = (n - 1)*d + a_1

given:

a_6 = 35 = (6-1)*d + a_1

a_13 = (13 -1)*d + a_1 = 77

find a_1

we have  35 = 5d + a_1

and  77 = 12d + a_1

2 equations in 2 unknowns.

We can solve this.

77 = 12d + a_1

35 = 5d + a_1

minus  the 2 equations from each other.

77 - 35 = 12d - 5d + a_1 - a_1

42 = 7d

d = 6

Find a_1

35 = 5*6 + a_1

35 = 30 + a_1

a_1 = 35 -30 = 5

a_1 = 5

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<h3>What does this problem require?</h3>

This problem requires you to calculate the perimeter and area of each field and based on this information you can find the total of the fence the farmer requires, the cost, and the number of sheep.

<h3>How to calculate the perimeter?</h3>

You can calculate the perimeter by adding all the sides.

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<h3>How to calculate the area?</h3>

To calculate the area, multiply the height by the width.

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The fencing needed is equal to the perimeter.

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  • Field 2: 60 m of fencing

<h3>How much will it cost?</h3>

Multiply the number of meters needed by the price per meter ( £16 per meter).

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To calculate this divide the area into the space required by each sheep (10m2).

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Note: This question is incomplete; here is the missing information:

Farmer Gump has two problems. His first problem is to work out how much fencing he needs to buy for his fields so his sheep don’t escape. His second problem is to work out how many sheep each field can hold—each sheep needs a minimum of 10m² of grass!

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