In a geometric sequence, if the first term is 2 and the common ratio is 3, what is the third term?

In a geometric sequence, if the first term is 2 and the common ratio is 3, what is the third term?

• A. 6
• B. 9
• C. 18
• D. 27

Answer: (C)

To find the third term of a geometric sequence, you can use the formula for the n-th term of a geometric sequence, which is given by: \[ a_n = a_1 \cdot r^{(n-1)} \] where \( a_n \) is the n-th term, \( a_1 \) is the first term, \( r \) is the common ratio, and \( n \) is the term number you want to find. In this case, the first term \( (a_1) \) is 2 and the common ratio \( (r) \) is 3. To find the third term \( (a_3) \), plug in the values: \[ a_3 = 2 \cdot 3^{(3-1)} = 2 \cdot 3^2 \] Calculating \( 3^2 \) gives 9, so: \[ a_3 = 2 \cdot 9 = 18 \] Thus, the third term of the geometric sequence is 18. This matches the correct answer, confirming that the calculations are accurate.

To find the third term of a geometric sequence, you can use the formula for the n-th term of a geometric sequence, which is given by:

[ a_n = a_1 \cdot r^{(n-1)} ]

where ( a_n ) is the n-th term, ( a_1 ) is the first term, ( r ) is the common ratio, and ( n ) is the term number you want to find.

In this case, the first term ( (a_1) ) is 2 and the common ratio ( (r) ) is 3. To find the third term ( (a_3) ), plug in the values:

[ a_3 = 2 \cdot 3^{(3-1)} = 2 \cdot 3^2 ]

Calculating ( 3^2 ) gives 9, so:

[ a_3 = 2 \cdot 9 = 18 ]

Thus, the third term of the geometric sequence is 18. This matches the correct answer, confirming that the calculations are accurate.