Identify the Sequence 11 , 22 , 44 , 88

Problem

11,22,44,88,…

Solution

1. Calculate the ratios between consecutive terms to determine if there is a common ratio.

(r_1)=22/11=2

(r_2)=44/22=2

(r_3)=88/44=2

2. Identify the type of sequence based on the constant ratio. Since each term is multiplied by 2 to get the next term, this is a geometric sequence.

3. Determine the first term (a_1) and the common ratio r

(a_1)=11

r=2

4. Apply the formula for the nth term of a geometric sequence, which is (a_n)=(a_1)⋅r(n−1)

(a_n)=11⋅2(n−1)

Final Answer

Geometric Sequence: *(a_n)=11⋅2(n−1)

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