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Math  /  Algebra

Question5. What are the first three terms of the Arithmetic Sequence an=11−3(n−1)?a_{n}=11-3(n-1) ? 0,8,160,8,16 11,8,511,8,5 1,2,31,2,3 8,5,28,5,2

Studdy Solution

STEP 1

1. The sequence given is an arithmetic sequence.
2. The formula for the n n -th term of the sequence is an=11−3(n−1) a_n = 11 - 3(n-1) .
3. We need to find the first three terms of the sequence.

STEP 2

1. Understand the formula for the arithmetic sequence.
2. Calculate the first term of the sequence.
3. Calculate the second term of the sequence.
4. Calculate the third term of the sequence.
5. Identify the correct sequence from the given options.

STEP 3

The formula an=11−3(n−1) a_n = 11 - 3(n-1) represents an arithmetic sequence where each term is calculated based on its position n n .

STEP 4

To find the first term (a1 a_1 ), substitute n=1 n = 1 into the formula:
a1=11−3(1−1)=11−3×0=11 a_1 = 11 - 3(1-1) = 11 - 3 \times 0 = 11

STEP 5

To find the second term (a2 a_2 ), substitute n=2 n = 2 into the formula:
a2=11−3(2−1)=11−3×1=11−3=8 a_2 = 11 - 3(2-1) = 11 - 3 \times 1 = 11 - 3 = 8

STEP 6

To find the third term (a3 a_3 ), substitute n=3 n = 3 into the formula:
a3=11−3(3−1)=11−3×2=11−6=5 a_3 = 11 - 3(3-1) = 11 - 3 \times 2 = 11 - 6 = 5

STEP 7

The first three terms of the sequence are 11,8,5 11, 8, 5 .
Among the given options, the correct sequence is:
11,8,5 \boxed{11, 8, 5}

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