Substituting a = 5 and r = 2 into the general formula gives the n^(th) term as a_n = 5 · 2^(n-1). For instance, the next term (5^(th) term) is 5 · 2^(4) = 5 · 16 = 80.

The sequence is 5, 10, 20, 40

Answer: Geometric Progression with first term $a = 5$ , common ratio $r = 2$ , and general term $a_n = 5 \cdot 2^{n-1}$ .

Step-by-step solution

Step 1: Check the ratio between consecutive terms

To determine the nature of the sequence, we compute the ratio between each term and the term preceding it. Since the ratio is constantly equal to $2$ , the sequence is a Geometric Progression (GP) with common ratio $r = 2$ .

Step 2: Identify the first term and general formula

The first term of the geometric progression is $a = 5$ , and the common ratio is $r = 2$ . The standard formula for the $n^{\text{th}}$ term of any geometric progression is given by $a_n = a r^{n-1}$ .

Step 3: Substitute values to find the nth term

Substituting $a = 5$ and $r = 2$ into the general formula gives the $n^{\text{th}}$ term as $a_n = 5 \cdot 2^{n-1}$ . For instance, the next term ( $5^{\text{th}}$ term) is $5 \cdot 2^{4} = 5 \cdot 16 = 80$ .

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