Q75 / 150 · MHT CET 2020 (16 Oct Shift 1) · Mathematics

If for an Arithmetic progression, 9 times nineth term is equal to 13 times thirteenth term, then value of twenty second term is

  • Correct answer
    A
    0
  • B
    2
  • C
    4
  • D
    5

Solution

Let the first term and common difference of given $\mathrm{AP}$ be a and d, respectively. Given $\begin{array}{l} 9 . a_{9}=13 . a_{13} \\ \Rightarrow 9[a+(9-1) d]=13[a+(13-1) d] \\ \Rightarrow 9[a+8 d]=13[a+12 d] \\ \Rightarrow 9 a+72 d=13 a+156 d \\ \Rightarrow 4 a+84 d=0 \\ \Rightarrow 4[a+21 d]=0 \\ \Rightarrow 4[a+(22-1) d=0 \\ \Rightarrow a+(22-1) d=0 \\ \Rightarrow a_{22}=0 \end{array}$

Hence, the correct answer is option: 'A'.

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