Correct option is **(C) The reminder is 1 when 931**^{th} term is divided by 2

Given sequence is

2,3,5,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,24,26......

2003^{rd} term = ?

1892^{th} term = 1937

1980^{th} term = 2026

2003^{rd} term = 2026 + (2003 - 1980)

= 2026 + 23 = 2049

870^{th} term = 901

930^{th} term = 962

\(\therefore\) 931^{st} term = 963

(a, b) \(\frac{T_{2003}}{2048}=\frac{2049}{2048}\) the reminder left 1

option (a), and (b) are false

(c, d) \(\frac{T_{931}}2=481+\frac12\)

Thus, reminder left 1

option (c) is correct