If a sequence has first term 5 and common ratio 3, what is a4?

If a sequence has first term 5 and common ratio 3, what is a4?

• A. 75
• B. 245
• C. 135
• D. 405

Answer: (C)

In a geometric sequence, each term is obtained by multiplying the previous term by the common ratio. Starting with a1 = 5 and r = 3, we get a2 = 5×3 = 15, a3 = 15×3 = 45, and a4 = 45×3 = 135. Using the formula a_n = a1 × r^(n−1), a4 = 5 × 3^3 = 5 × 27 = 135. So the value is 135. (For reference, a5 would be 135×3 = 405, which is why that number appears in the options, but it corresponds to the fifth term, not the fourth.)

In a geometric sequence, each term is obtained by multiplying the previous term by the common ratio. Starting with a1 = 5 and r = 3, we get a2 = 5×3 = 15, a3 = 15×3 = 45, and a4 = 45×3 = 135. Using the formula a_n = a1 × r^(n−1), a4 = 5 × 3^3 = 5 × 27 = 135. So the value is 135. (For reference, a5 would be 135×3 = 405, which is why that number appears in the options, but it corresponds to the fifth term, not the fourth.)