- #1
Suraj M
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Homework Statement
The ratio of sums of 2 AP for n terms each is ## \frac{3n + 8}{7n + 15}##
that is
$$ {\frac{s_a}{s_b}} = \frac{3n + 8}{7n + 15} $$
find the ratio of their 12th terms.
$$ Required= \frac{a₁_a+(n-1)d_a}{a_b + (n-1)d_b}$$
Homework Equations
Tn = a + (n-1)d
The Attempt at a Solution
OKay the regular way that gives the right answer is this..
$$ {\frac{2a_a + (n-1)d_a}{2a_b + (n-1)d_b} } = {\frac{3n + 8}{7n + 15}} ~~ eq1 ~~$$
$$required = \frac{a_a+11d_a}{a_b+11d_b} $$
so putting n = 23 in the eq 1 we get the answer as ## \frac{7}{16} ##
but i tried another method..
$${\frac{s_a}{s_b}} ={ \frac{3n + 8}{7n + 15}}$$
here we can say..
$$ s_a = (3n + 8)x $$
$$ s_b = (7n + 15)x $$
if i put n = 1 ,2 ,3 for both these AP's
for AP 1: using sa
s₁=a₁ right??
then a₁=11x
then s₂=14x so a₂ = s2 -s1 = 3x
then s3 =17x so a3 = s3-s2 = 3x
how is a2=a3 ??
similarly even for AP2
but why??
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