Ageometric sequence is defined by the general term tn = 75(5n), where n ∈n and n ≥ 1. what is the recursive formula of the sequence? a) t1 = 75, tn = 5tn - 1, where n ∈n and n > 1 b) t1 = 75, tn = 75tn - 1, where n ∈n and n > 1 c) t1 = 375, tn = 5tn - 1, where n ∈n and n > 1 d) t1 = 375, tn = 5tn + 1, where n ∈n and n > 1

The correct answer is C) t₁ = 375, .

From the general form,
, we must work backward to find t₁.

The general form is derived from the explicit form, which is
.  We can see that r = 5; 5 has the exponent, so that is what is multiplied by every time. This gives us



Using the products of exponents, we can "split up" the exponent:


We know that 5⁻¹ = 1/5, so this gives us


Comparing this to our general form, we see that


Multiplying by 5 on both sides, we get that
t₁ = 75*5 = 375

The recursive formula for a geometric sequence is given by
, while we must state what t₁ is; this gives us

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