Final answer:
To find the value of 4 in a geometric sequence with a₁ = 40 and a₇ = 160, use the formula aₙ = a₁ * r^(n-1), where r is the common ratio. After solving for r, multiply the previous term by r to find the value of 4.
Step-by-step explanation:
A geometric sequence is a sequence in which each term is found by multiplying the previous term by a constant ratio. To find the value of 4 in the geometric sequence with a1 = 40 and a7 = 160, we can use the formula for the nth term of a geometric sequence: an = a1 * r^(n-1). We know that a1 = 40 and a7 = 160. Plugging these values into the formula, we can solve for r: 160 = 40 * r^(7-1). Dividing both sides by 40, we get 4 = r^6. Taking the sixth root of both sides, we find that r = 2. Therefore, the value of 4 in the sequence is found by multiplying the previous term (a3 = 40 * 2^2 = 160) by the constant ratio: 160 * 2 = 320.