Question

What is the 103rd term of the arithmetic sequence

Answer 1

ans: B: 31/4   is the 103rd term of the arithmetic sequence

Answer 2

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

$\frac{-2}{3} -\frac{-3}{4} = \frac{-8}{12} +\frac{9}{12} =\frac{1}{12}$

common difference is 1/12

now we need to find 103rd term

$a_n = a_1 + (n-1) d$

First term is -3/4, d= 1/12

$a_{103} = \frac{-3}{4}+(103-1)\frac{1}{12}$

$a_{103} = \frac{-3}{4}+(102)\frac{1}{12}$

$a_{103} = \frac{-3}{4}+\frac{34}{4}$

$a_{103} = \frac{-3+34}{4}$

$a_{103} = \frac{31}{4}$