Question

if (1+3+5+....+n terms)/1+2+3+...n terms) = 12/7 what is the value of n

Answer 1

Step-by-step explanation:

For first AP:

a = 1, d = 3-1 = 2

For Second AP:

a = 1, d = 2-1 = 1

$\frac{sum \: of \: n \: terms \: of \: 1st \: a.p. }{sum \: of \: n \: terms \: of \: 2nd \: a.p. } = \frac{12}{7}$

$\frac{ \frac{n}{2}(2a +(n - 1)d)}{ \frac{n}{2}(2a+(n - 1)d)} = \frac{12}{7}$

$\frac{(2 \times 1 + (n - 1) \times 2)}{(2 \times 1 + (n - 1) \times 1)} = \frac{12}{7}$

$\frac{(2 + 2n - 2) }{(2 + n - 1)} = \frac{12}{7}$

$\frac{2n}{n + 1} = \frac{12}{7}$

$14n \: = 12n + 12$

$14n - 12n = 12$

$2n = 12$

$n = \frac{12}{2}$

$n = 6$

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