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If the first difference of a sequence is the arithmetic sequence 2, 4, 6, 8, 10,...Find the first six terms of the original sequence in each of the following cases?

Respuesta :

SaniShahbaz

Step-by-step explanation:

The first differences being [tex]2, 4, 6, 8, 10,...[/tex]  means

  • 2 is the difference between the 1st and 2nd terms
  • 4 is the difference between the 2nd and 3rd terms
  • 6 is the difference between the 3rd and 4th terms
  • 8 is the difference between the 4th and 5th terms
  • 10 is the difference between the 5th and 6th terms

So,

If

The first term of the sequence is 2.

then

The second term of the sequence is [tex]2 + 2 = 4[/tex]

The Third term of the sequence is [tex]4 + 4 = 8[/tex]

The Fourth term of the sequence is [tex]8 + 6 = 14[/tex]

The Fifth term of the sequence is [tex]14 + 8 = 22[/tex]

The Sixth term of the sequence is [tex]22 + 10 = 32[/tex]

Keywords: sequence, arithmetic sequence

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