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Mathematical Induction — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSMathematical Induction1 Mark
MCQ
If $10^\text{n} + 3 \times 4^{\text{n}+2}+\lambda$ is divisible by 9 for all $\text{n}\in\text{N},$ then the least positive integer value of $\lambda$ is
  • ✓
    5
  • B
    3
  • C
    7
  • D
    1
✓

Answer

Correct option: A.
5
Given,
$10\text{n }+3\times^{\text{n}+2}+\lambda$ is divisible by 9,
$\text{P}(1)=10^1+3\times4^{1+2}+\lambda$ is exactly divisible by 9 then the value of $\lambda$ is 5.

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