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  • 24-09-2020
  • Mathematics
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Given that the 3rd term in an arithmetic sequence is -2 and the 7th term is -10, tell me what the 1st term in the sequence is. Explain how you know.

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MathPhys
MathPhys MathPhys
  • 24-09-2020

Answer:

2

Step-by-step explanation:

a₃ = -2

a₇ = -10

The nth term of an arithmetic sequence is:

a = a₁ + d (n − 1)

Therefore:

-2 = a₁ + d (3 − 1) = a₁ + 2d

-10 = a₁ + d (7 − 1) = a₁ + 6d

Subtract the equations:

8 = -4d

d = -2

Plug into either equation to find the first term.

-2 = a₁ + 2(-2)

a₁ = 2

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