In a geometric sequence with a1 = 4 and r = -3, find a4.

In a geometric sequence with a1 = 4 and r = -3, find a4.

• A. 108
• B. -36
• C. 72
• D. -108

Answer: (D)

In a geometric sequence, each term is found by multiplying the previous term by the common ratio, so the nth term is a_n = a1 × r^(n−1). With a1 = 4 and r = −3, the fourth term is a4 = 4 × (−3)^(4−1) = 4 × (−3)^3 = 4 × (−27) = −108. You can check by stepping through: a2 = 4 × (−3) = −12, a3 = −12 × (−3) = 36, a4 = 36 × (−3) = −108. So the value is −108.

In a geometric sequence, each term is found by multiplying the previous term by the common ratio, so the nth term is a_n = a1 × r^(n−1). With a1 = 4 and r = −3, the fourth term is a4 = 4 × (−3)^(4−1) = 4 × (−3)^3 = 4 × (−27) = −108. You can check by stepping through: a2 = 4 × (−3) = −12, a3 = −12 × (−3) = 36, a4 = 36 × (−3) = −108. So the value is −108.