Identify the Sequence 11 , 44 , 176 , 704

Problem

11,44,176,704,…

Solution

1. Calculate the ratio between the first two terms by dividing the second term by the first term.

44/11=4

2. Verify the ratio between the subsequent terms to see if it remains constant.

176/44=4

704/176=4

3. Identify the type of sequence based on the constant ratio. Since each term is multiplied by 4 to get the next term, this is a geometric sequence.

4. Determine the parameters of the sequence where the first term (a_1) is 11 and the common ratio r is 4

(a_1)=11

r=4

5. State the general formula for the nth term of this geometric sequence.

(a_n)=(a_1)⋅r(n−1)

(a_n)=11⋅4(n−1)

Final Answer

Geometric Sequence with *(a_1)=11,r=4

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