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Elis [28]
3 years ago
7

Here are the first four terms of a sequence.

Mathematics
1 answer:
Nataly_w [17]3 years ago
8 0

Answer:

  • aₙ = 2n² + n + 1

Step-by-step explanation:

We observe that the difference of terms is 4, 7 and 15 and next level difference is 4. It means the sequence is quadratic.

<u>We can compare this with simple quadratic sequence </u>

  • 1, 4, 9, 16

<u>and find out that doubling each term gives us </u>

  • 2, 8, 18, 32

This is close to our sequence, write the terms as follows to find exact rule

<u>The first term: </u>

  • a₁ = 4  = 2*1² + 2 = 2*1² + 1 + 1

<u>The second term</u>

  • a₂ = 11  = 2*2² + 3 = 2*2² + 2 + 1

<u>The third term:</u>

  • a₃ = 22 = 2*3² + 4 = 2*3² + 3 + 1

<u>The fourth term:</u>

  • a₄ = 37 = 2*4² + 5 = 2*4² + 4 + 1

<u>The nth term as per observation above is:</u>

  • aₙ = 2n² + n + 1
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