Question

The common ratio of a geometric sequence is 1/2, and the fourth term is 1/4 What is the third term of the sequence?​

Answer 1

Answer:

third term is 1/2

Step-by-step explanation:

common ratio =r=1/2

t4=1/4

tn=a r^n-1

t4=a (1/2)^4-1

1/4=a (1/2)³

1/4=a ×1/8

a. =1/4×8

a. =2

t3=a r^3-1

t3=2×(1/2)²

t3=2×1/4

t3=1/2

Answer 2

Given:

Common ratio, r = $\frac{1}{2}$

Fourth term, $t_{4}$ = $\frac{1}{4}$

To find :

The third term of the sequence.

Formula to be used:

$t_{n} = ar^{n - 1}$

Solution:

Step 1 of 2:

Substitute the values of r and $t_{4}$ in the following formula ,

$t_{n} = ar^{n - 1}$

$t_{4}$ = a $(\frac{1}{2}) ^{4-1}$

$t_{4} = \frac{1}{4}$ ,

$\frac{1}{4 } = a (\frac{1}{2}) ^3}$

$\frac{1}{4 } = a (\frac{1}{8}) }$

a = $\frac{1}{4}$ × 8

a = 2

Step 2 of 2:

To find the third term of the sequence,

$t_{n} = ar^{n - 1}$

$t_{3} =$ $2(\frac{1}{2}) ^{3-1}$

$t_{3} =$ $2(\frac{1}{2}) ^{2}$

$t_{3} = 2(\frac{1}{4})$

$t_{3} = \frac{1}{2}$

Final answer:

The third term of the sequence is $\frac{1}{2}$ .