Question

a geometric sequence has a common ration(r) of 3 and the 8th term (a₈) is 13,122. what is the first term of the sequence (a₁)?

Explanation:

Step1: Recall geometric term formula

The nth term of a geometric sequence is given by $a_n = a_1 r^{n-1}$

Step2: Plug in known values

We know $a_8=13122$, $r=3$, $n=8$. Substitute into the formula:
$13122 = a_1 \times 3^{8-1}$

Step3: Calculate $3^7$

$3^7 = 2187$

Step4: Solve for $a_1$

Rearrange to isolate $a_1$: $a_1 = \frac{13122}{2187}$

Step5: Compute the quotient

$\frac{13122}{2187} = 6$

Answer:

6