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just olya [345]
3 years ago
9

An arithmetic sequence has this recursive formula: (a^1 =8, a^n= a^n-1 -6

Mathematics
1 answer:
eduard3 years ago
3 0

Answer:

a_n = 8 + (n - 1) (-6)

Step-by-step explanation:

Given

a_1 = 8

Recursive: a_{n} = a_{n-1} - 6

Required

Determine the formula

Substitute 2 for n to determine a_2

a_{2} = a_{2-1} - 6

a_{2} = a_{1} - 6

Substitute a_1 = 8

a_2 = 8 - 6

a_2 = 2

Next is to determine the common difference, d;

d = a_2 - a_1

d = 2 - 8

d = -6

The nth term of an arithmetic sequence is calculated as

a_n = a_1 + (n - 1)d

Substitute a_1 = 8 and d = -6

a_n = a_1 + (n - 1)d

a_n = 8 + (n - 1) (-6)

Hence, the nth term of the sequence can be calculated usinga_n = 8 + (n - 1) (-6)

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