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8. sequence and series — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS8. sequence and series1 Mark
MCQ
${n^{th}}$ term of the series$1 + \frac{4}{5} + \frac{7}{{{5^2}}} + \frac{{10}}{{{5^3}}} + ........$ will be
  • A
    $\frac{{3n + 1}}{{{5^{n - 1}}}}$
  • B
    $\frac{{3n - 1}}{{{5^n}}}$
  • ✓
    $\frac{{3n - 2}}{{{5^{n - 1}}}}$
  • D
    $\frac{{3n + 2}}{{{5^{n - 1}}}}$
✓

Answer

Correct option: C.
$\frac{{3n - 2}}{{{5^{n - 1}}}}$
c
(c) This series is clearly an $A.G.$, the corresponding $A.P.$ is $1 + 4 + 7 + 10 + .........$ having ${n^{th}}$ term $ = 3n - 2$

and corresponding $G.P.$ is $1 + \frac{1}{5} + \frac{1}{{{5^2}}} + .........$ having ${n^{th}}$ term $ = \frac{1}{{{5^{n - 1}}}}$

Hence required ${n^{th}}$ term of the series is $\frac{{3n - 2}}{{{5^{n - 1}}}}$.

Trick : Check by putting $n = 1,\;2$ in alternates.

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