Question

3. Which of these sequences whose nth term, for n > 1, is given below has all positive terms? (4 points) a= O. O.-48 Ic ne2 a 0.- as a fraction. (4 points) 4. Write the recurring decimal 0.ababab O a+b 99 O a.b 99 O 10b+a 99 O 10a+b 99

Answer 1

Answer 3.

Option D is correct

Because in  $a_n =(- \frac{1}{2})^{2n}$ power of -1/2 is 2n which is always even for any values of n and

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

Or, $a_n =(-1)^{2n}[ \frac{1}{2}]^{2n}$ and so

$a_n = (\frac{1}{2})^{2n}$ is always positive.

Answer 4.

Let x = 0.ababab...

so 100x = ab.ababab....

substract x from 100x

so, 99x = (ab.abababa....)-(0.ababab...)

Or, 99x = ab

so, x = ab/99

or $0.ababab....=\frac{a*b}{99}$ 2nd option