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Akimi4 [234]
3 years ago
5

The term to term rule for a sequence is Multiply by 2 the sequence starts a 2a ___ ___ the total value of the first three terms

is 63 work out the total value of the first four terms
Mathematics
1 answer:
Lostsunrise [7]3 years ago
7 0

Answer:

135

Step-by-step explanation:

The sequence are:

a, 2a, 4a, 8a, 16a.....

the total value of the first three terms is 63

That is,

a + 2a + 4a = 63

7a = 63

a = 63/7

a = 9

work out the total value of the first four terms

First four terms are: a, 2a, 4a, 8a

Where,

First term, a = 9

Second term, 2a = 2*9 = 18

Third term, 4a = 4*9 = 36

Fourth term, 8a = 8*9 = 72

The total value of the first four terms = 9 + 18 + 36 + 72

= 135

The total value of the first four terms = 135

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There are five consecutive odd integers. The sum of the three smallest is 3 more than the sum of the two largest. Find the integ
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Answer:

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Step-by-step explanation:

We will solve this word problem using 2k+1 which is one of the general forms of an odd integer.

Let 2k+1 be the first odd integer.

(2k+1) + (2k+3) + (2k +5) =  (2k+7) + (2k +9) + 3 (the +3 is to accommodate for the left side being 3 more than the right)

Solve for k

6k + 9 = 4k + 19

6k - 4k + 9 = 4k-4k + 19

2k + 9 = 19

2k + 9 - 9 = 19 - 9

2k = 10

2k/2 = 10/2

k = 5

To get the first digit in the series plug in 5 for k

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2(5) + 1

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So our series is 11, 13, 15, 17, 19

Let's test it.

11 + 13 +15 = 39

17 + 19 = 36

So we are correct, the first 3 integers are 3 more that the sum of the last 2.

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Step-by-step explanation:

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