Math  /  Algebra

QuestionWhat is the next term of the geometric sequence? 2,10,502,10,50 \square

Studdy Solution

STEP 1

1. This is a geometric sequence, meaning each term is obtained by multiplying the previous term by a constant ratio.
2. We need to find the common ratio and then use it to determine the next term in the sequence.

STEP 2

1. Identify the common ratio of the geometric sequence.
2. Use the common ratio to find the next term in the sequence.

STEP 3

Identify the common ratio rr by dividing the second term by the first term.
r=102=5 r = \frac{10}{2} = 5

STEP 4

Confirm the common ratio rr by dividing the third term by the second term to ensure consistency.
r=5010=5 r = \frac{50}{10} = 5

STEP 5

Use the common ratio r=5r = 5 to find the next term in the sequence by multiplying the last known term (50) by the common ratio.
Next term=50×5=250 \text{Next term} = 50 \times 5 = 250
Therefore, the next term of the geometric sequence 2,10,502, 10, 50 is 250250.

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