Question

Find the first term and the explicit formula a12=1/32 and r=1/2

Answer 1

Answer:

see explanation

Step-by-step explanation:

The n th term of a geometric sequence is

$a_{n}$ = a$(r)^{n-1}$

where a is the first term and r the common ratio

Given $a_{12}$ = $\frac{1}{32}$ and r = $\frac{1}{2}$, then

a $(\frac{1}{2}) ^{11}$ = $\frac{1}{32}$, that is

$\frac{a}{2^{11} }$ = $\frac{1}{32}$

$\frac{a}{2048}$ = $\frac{1}{32}$ ( cross- multiply )

32a = 2048 ( divide both sides by 32 )

a = 64 ← first term

Thus the explicit formula is

$a_{n}$ = 64 $(\frac{1}{2}) ^{n-1}$