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Katarina [22]
3 years ago
10

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. E

xplain how you know.
Mathematics
1 answer:
Elenna [48]3 years ago
5 0

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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