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8. Sequences and Series
easy
જો $\frac{{3 + 5 + 7 + ..........n\; }}{{5 + 8 + 11 + .........10\; }}$ $ = 7\,,\,\,$ તો $n$ ની કિમત મેળવો $?$
A
$35$
B
$36$
C
$37$
D
$40$
Solution
$\frac{{3 + 5 + 7 + ……….n\; }}{{5 + 8 + 11 + ………10\; }}$ $ = 7\,,\,\,$ આપેલ છે.
$ \Rightarrow \frac{{\frac{n}{2}[6 + (n – 1)2]}}{{\frac{{10}}{2}[10 + (10 – 1)3]}} = 7 \Rightarrow \frac{{n(2n + 4)}}{{10 \times 37}} = 7$
$ \Rightarrow {n^2} + 2n – 1295 = 0 \Rightarrow (n + 37)(n – 35) = 0$ તેથી ${\text{n = 35}}$.
Standard 11
Mathematics
