the common ratio of a geometric series is 3 and the fifth term is 324. What is the value of the first term?
6 years ago
Answered By Kazi A
Let's look at the definition of a geometric series, and see how we can use it to solve this problem.
A geometric series is a series of numbers defined in terms of a ratio (r) and a first term ( $t_0$t0 ) by the relation:
$t_n=t_0\cdot r^n$tn=t0·rn
Interpretation of the above formula: To get the the $n^{th}$nth term, you simply multiply $t_0$t0 by $r^n$rn . In this case, we are given the $5^{th}$5th term, so n = 5, and its value is $t_5=324$t5=324. We are also given the ratio, r =3. Therefore:
6 years ago
Answered By Kazi A
Let's look at the definition of a geometric series, and see how we can use it to solve this problem.
A geometric series is a series of numbers defined in terms of a ratio (r) and a first term ( $t_0$t0 ) by the relation:
$t_n=t_0\cdot r^n$tn=t0·rn
Interpretation of the above formula: To get the the $n^{th}$nth term, you simply multiply $t_0$t0 by $r^n$rn . In this case, we are given the $5^{th}$5th term, so n = 5, and its value is $t_5=324$t5=324. We are also given the ratio, r =3. Therefore:
$324=t_0\cdot3^5\rightarrow t_0=\frac{324}{3^5}=\frac{324}{243}$324=t0·35→t0=32435 =324243