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. (b)

Solution:

  1. 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 $=Q _{r+1}-Q _r=6$



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