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SEQUENCES AND SERIES — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSEQUENCES AND SERIES1 Mark
MCQ
How many terms of G.P. 2,4,8,16, …………… are required to give sum 254?
  • A
    4
  • B
    5
  • C
    6
  • ✓
    7
✓

Answer

Correct option: D.
7
  1. 7
Solution:
$=2$ and
$r=\frac{4}{2}=2.$
We know$\text{s}_\text{n}=\text{a}\frac{(\text{r}^\text{n}-1)}{\text{(r}-1)}$
$2\frac{(2^\text{n-1)}}{(2-1)}=254$
$\Rightarrow 2^n- 1 = 127 \Rightarrow 2^n = 128 = 2^7$
$\Rightarrow n = 7$.

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