JEE Advanced2007MathematicsSequences and SeriesActual
Paragraph: Let V_r denotes the sum of the first r terms of an arithmetic progression (A P) whose first term is r and the common difference is (2 r-1) . Let T_r=V_ r+1 -V_r-2 and Q_r=T_ r+1 -T_r for r=1,2, Question: T_r is always
Options
- Aan odd number
- Ban even number
- Ca prime number
- Da composite number
Correct answer
D. a composite number
Step-by-step solution
V_ r+1 -V_r=(r+1)^3-r^3- 1 2 [(r+1)^2-r^2 ]+ 1 2 (1) aligned & =3 r^2+2 r+1 T_r & =3 r^2+2 r-1=(r+1)(3 r-1) aligned which is a composite number.