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Tom [10]
3 years ago
15

A sequence of 7 numbers starts with 8. The second number in the sequence is unknown and may be positive or negative. The third t

hrough seventh numbers are the sum of the previous two numbers in the sequence, and the seventh number is 0. What is the sum of the 7 numbers?
Mathematics
1 answer:
scoray [572]3 years ago
8 0

Answer:

4

Explanation:

a_1=8,a_7=0

Since the third term is the sum of the two previous terms

a_3=a_2+a_1

a_7=a_6+a_5

a_7=a_5+a_4+a_4+a_3

Continuing in like manner

a_7=5a_3+3a_2

Since a_3=a_2+a_1

a_7=5(a_2+a_1+3a_2

a_7=5a_2+5a_1+3a_2

a_7=8a_2+5a_1

Recall: a_1=8,a_7=0

0=8a_2+5*8

8a_2=-40

a_2=-5

The sequence is therefore:

8,-5,3,-2,1,-1,0

The sum of the seven numbers is 4.

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