Identify the Sequence 5 , 20 , 80 , 320

Problem

5,20,80,320,…

Solution

1. Calculate the ratio between the second term and the first term.

20/5=4

2. Calculate the ratio between the third term and the second term.

80/20=4

3. Calculate the ratio between the fourth term and the third term.

320/80=4

4. Identify the type of sequence based on the constant ratio. Since there is a common ratio r=4 the sequence is geometric.

5. Determine the general formula for the nth term using the first term (a_1)=5 and the common ratio r=4

(a_n)=(a_1)⋅r(n−1)

Final Answer

Geometric Sequence with *(a_1)=5,r=4

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