Sequences and Series 2 Question 13
14. Which one of the following is a correct statement?
(a) $Q _1, Q _2, Q _3, \ldots$ are in an AP with common difference 5
(b) $Q _1, Q _2, Q _3, \ldots$ are in an AP with common difference 6
(c) $Q _1, Q _2, Q _3, \ldots$ are in an AP with common difference 11
(d) $Q _1=Q _2=Q _3=\ldots$
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Answer:
Correct Answer: 14. $\beta \in-\infty, \frac{1}{3}$ and $\gamma \in-\frac{1}{27}, \infty$
Solution:
- Since, $T _r=3 r^{2}+2 r-1$
and $T _{r+1}=3(r+1)^{2}+2(r+1)-1$
$\therefore \quad Q _r=T _{r+1}-T _r=3[2 r+1]+2[1]$
$\Rightarrow Q _r=6 r+5$
$\Rightarrow \quad Q _{r+1}=6(r+1)+5$
Common difference $=Q _{r+1}-Q _r=6$
