Question

For a given geometric sequence, the 9th term, a9, is equal to 43/256 and the 14th term, a14, is equal to 172. Find the value of the 18 term

Answer 1

Answer:

$18th=44032$

Step-by-step explanation:

From the question we are told that:

9th term $a9=\frac{43}{256}$

14th term $a14=172$

Generally the equation for Geometric sequence is mathematically given by

 $a_n=a_1r^{n-1}$

For 9th term

 $\frac{43}{256}=a_1r^{8}$

For 14th term

 $172=a_1r^{13} \\a_1=\frac{172}{r^13}$

Substitute in 9th term

 $\frac{43}{256}=\frac{172}{r^13}*r^{8}$

 $\frac{43}{256*172}=r^{-5}$

 $r=^5sqrt{\frac{44032}{43}}$

 $r=4$

Therefore First term a is given as

 $a_1=\frac{172}{4^13}$

 $a_1=2.563*10^{-6}$

Generally the equation for the 18th term is mathematically given by

 $18th=a_1r^{17}$

 $18th=2.563*10^{-6}*4^{17}$

 $18th=44032$