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chubhunter [2.5K]
3 years ago
6

A pattern exists among the units digit of the posers of 8 as shown in the diagram.

Mathematics
1 answer:
guajiro [1.7K]3 years ago
4 0

Answer:

B) 4

Step-by-step explanation:

We can solve this by observing some pattern.

The powers ending in 4 as unit digit are:

{8}^{2} , {8}^{6} , {8}^{10} , {8}^{14} , {8}^{20} ,...

The exponents form the sequence:

2,6,10,14,20,...

We need to check if 62 belongs to this sequence.

This is an arithmetic sequence with a common difference of 4 and a first term of 2.

The explicit formula is

2 + 4(n - 1)

We equate this to 62 and solve for n.

2 + 4(n - 1) = 62 \\ 4(n - 1) = 60 \\ n - 1 = 15 \\ n = 16

Since n is a natural number, 62 belongs to the sequence.

Hence

{8}^{62}

will have a unit digit of 4.

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