Question

how would i find the missing term of the geometric series
a1 = 4, an = 324, r = 3

Answer 1

well it looks like you need to find the number of terms n

use

\[T_{n} = ar^{n-1}\]

then

\[324 = 4 \times 3^{n -1}\]

you need to solve for n

divide both sides by 4

\[\frac{324}{4} = 3^{n -1}\]

or

\[81 = 3^{n -1} \]

express 81 as a power of 3

\[3^4 = 3^{n -1}\]

equate the powers

4 = n - 1

I'll let you finish the question

Answer 2

ok thanks