Gujarat BoardEnglish MediumSTD 11 CommerceStatisticsGeometric progression3 Marks
Question
If for a $G.P.$, $\mathrm{T}_{n}=80, \mathrm{~S}_{n}=157.5$ and $r=2$, find $a$ and $n$.
✓
Answer
Here, values of $\mathrm{T}_n$ and $\mathrm{S}_n$ are given, so we shall use the formula
$\mathrm{S}_n=\frac{r T_m-a}{r-1}
$Putting the values of $T_n, r$ and $S_n$ in $S_e=\frac{r T_n-a}{r-1}$
$\therefore 157.5=\frac{2 \times 80-a}{2-1}$
$\therefore 157.5=160-a$
$\therefore a=160-157.5$
$\therefore a=2.5$
$\text { Now } T_s=a r^{n-1}$
$\therefore 80=2.5 \times(2)^{-1}$
$\therefore 2^{n-1}=32$
$\therefore 2^{-1}=2^5$
Equating the powers on both the sides, we get
$n-1=5$
$\therefore n n$
Thus, $a=2.5$ and $n=6$
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