Is this the recursive formula for geometric sequences?\begin{cases}a_1=first\ term\\a_n=r\times a_{n-1}\end{cases}

keche0b 2022-01-04 Answered

Is this the recursive formula for geometric sequences?
{a1=first terman=r×an1

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Vivian Soares
Answered 2022-01-05 Author has 36 answers

We have
{a1=first terman=r×an1The second term of this sequence isa2=r×a21a2=r×a1 (2)The third term:a3=r×a31a3=r×a2Put value of a2 from equation 2a3=r×(r×a1)a3=r2×a1(3)Similarly, you can calculate a4a4=r×a41a4=r×a3Put a value of a3 from the equation (3)a4=r×(r2×a1)a4=r3×a1 (4)And so on. Thus, we have the followinga1,r×a1,r2×a1,....So we have observed thata2a1=a3a2=a4a3=...=anan1=r
Thus, it's the formula of geometric sequences.

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