The common difference of the A.P. $$\frac{1}{3},$$ $$\frac{{1 - 3b}}{3},$$ $$\frac{{1 - 6b}}{3},$$ . . . . . . is
A. $$\frac{1}{3}$$
B. $$ - \frac{1}{3}$$
C. $$ - b$$
D. $$b$$
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\text{A}}{\text{.P}}{\text{.is}}\,\,\frac{1}{3},\,\frac{{1 - 3b}}{3},\,\frac{{1 - 6b}}{3},\,...... \cr & \Rightarrow \frac{1}{3},\,\frac{1}{3} - \frac{{3b}}{3},\,\frac{1}{3} - \frac{{6b}}{3},\,...... \cr & \Rightarrow \frac{1}{3},\,\frac{1}{3} - b,\,\frac{1}{3} - 2b,\,....... \cr & \therefore d = \left( {\frac{1}{3} - b} \right) - \frac{1}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{3} - b - \frac{1}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = - b \cr} $$Related Questions on Progressions
Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.
A. 5
B. 6
C. 4
D. 3
E. 7
The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is
A. 600
B. 765
C. 640
D. 680
E. 690
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