Answer:
option B: 31/4
Step-by-step explanation:
Given
-3/4, -2/3 , -7/12, -1/2...........
General formula for arithmeti sequence to find nth term is
a_n = a_1 + (n-1) d
first term a_1 = -3/4
We find out common difference 'd'
Lets find the difference of first two terms
[tex]\frac{-2}{3} -\frac{-3}{4} = \frac{-8}{12} +\frac{9}{12} =\frac{1}{12}[/tex]
common difference is 1/12
now we need to find 103rd term
[tex]a_n = a_1 + (n-1) d[/tex]
First term is -3/4, d= 1/12
[tex]a_{103} = \frac{-3}{4}+(103-1)\frac{1}{12}[/tex]
[tex]a_{103} = \frac{-3}{4}+(102)\frac{1}{12}[/tex]
[tex]a_{103} = \frac{-3}{4}+\frac{34}{4}[/tex]
[tex]a_{103} = \frac{-3+34}{4}[/tex]
[tex]a_{103} = \frac{31}{4}[/tex]
