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If {S}_{n}={(4)}^{n}+3, what is the units digit of {S}_{100}?

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If $S_{n} = (4)^{n} + 3$ , what is the units digit of $S_{100}$ ?

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Oliver Discussed

S_{n} = (4)^{n} + 3

, what is the units digit of

S_{100}

11 mins ago

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11 mins ago

Text solutionVerified

Begin by listing the first few terms of the sequence in order to find the pattern:

S_{1} = 4^{1} + 3 = 4 + 3 = 7

S_{2} = 4^{2} + 3 = 16 + 3 = 19

S_{3} = 4^{3} + 3 = 64 + 3 = 67

S_{4} = 4^{4} + 3 = 256 + 3 = 259

The units digit of all odd-numbered terms is

7

The units digit of all even-numbered terms is

9

Because

S_{100}

is an even-numbered term, its units digit will be

9

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Question Text	If $S_{n} = (4)^{n} + 3$ , what is the units digit of $S_{100}$ ?
Answer Type	Text solution:1
Upvotes	150