SEQUENCES AND SERIES — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSEQUENCES AND SERIES3 Marks
Question
Insert two numbers between 3 and 81, so that resulting sequence is GP.
✓
Answer
Let the two numbers be $a$ and $b$, then $3, a, b, 81$ are in GP.
$\because n^{\text {th }} \text { term, } T_n=A r^{n-1}$
$\therefore T_4=81=3 r^{4-1} \Rightarrow r^3=\frac{81}{3}$
$\Rightarrow r^3=27 \Rightarrow r^3=3^3$
On comparing the base of power 3 from both sides, we get
$r=3$
$\therefore a=A r=3 \times 3=9$
$\text { and } b=A r^2=3 \times 3^2=27$
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