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SEQUENCES AND SERIES — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSEQUENCES AND SERIES1 Mark
MCQ
Choose the correct answer. If 9 times the 9th term of an A.P. is equal to 13 times the $13^{th}$ term, then the 22nd term of the A.P. is:
  • ✓
    0
  • B
    22
  • C
    198
  • D
    220
✓

Answer

Correct option: A.
0
  1. 0
Solution:
Let the first term and common difference of given A.P. be a and d, respectively.
It is given that $9 \times \mathrm{t}_9=13 \times \mathrm{t}_{13}$
$\Rightarrow 9(a+8 d)=13(a+12 d)$
$\Rightarrow 9 a+72 d=13 a+156 d$
$\Rightarrow 4 a+84 d=0$
$\Rightarrow 4(a+21 d)=0$
$\Rightarrow t_{22}=0$

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