Question

for an AP a= 6and s10=195 show that Sn-3:Sn-8=n(n-3):(n-5)(n-8)

Answer 1

a = 6
Sn = n/2(2a+(n-1)d)
S10 = 10/2(12+9d) = 195
5(12+9d) = 195
9d = 39-12
d = 27/9
d = 3.
S(n-3) (n-3)/2(12+(n-3-1)3)
---------- = -----------------------------
S(n-8) (n-8)/2(12+(n-8-1)3)

S(n-3) (n-3)/2(12+(n-4)3)
---------- = -----------------------------
S(n-8) (n-8)/2(12+(n-9)3)

S(n-3). (n-3)(12+3n-12)
---------- = --------------------
S(n-8) (n-8)(12+3n-27)

S(n-3) (n-3)(3n)
---------- = --------------
S(n-8) (n-8)(3n-15)

S(n-3) 3n²-9n
---------- = -----------------
S(n-8). 3n²-39n+120

S(n-3) 3n(n-3)
---------- = -----------------
S(n-8). 3(n²-13n+40)

S(n-3). n(n-3)
---------- = -----------------
S(n-8). (n-5)(n-8)
Hope it helps you.
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