If f(x) is a function such that f(x – 1) + f(x + 1) = 
f(x) and f(5) = 8, then 
f(5 + 12r) = …..
Text Solution
Verified by Experts2008
Ans. 2008
Sol. Given, f(x – 1) + f(x + 1) = 
f(x) …(1)
from (1), f(x + 1) + f(x + 3) = 
f(x + 2) …(2)
adding (1) and (2)
f(x – 1) + f(x + 3) + 2f(x + 1) = 
[f(x) + f(x + 2)]
= 
. 
f(x + 1)
∴ f(x – 1) + f(x + 3) = f(x + 1) … (3)
⇒ f(x + 1) + f(x + 5) = f(x + 3) … (4)
adding (3) & (4)
f(x – 1) + f(x + 1) + f(x + 3) + f(x + 5)
= f(x + 1) + f(x + 3)
⇒ f(x – 1) = – f(x + 5)
⇒ f(x) = – f(x + 6) …(5)
⇒ f(x + 12) = f(x)
Now 
f(5 + 12r) = f(5) + f(5 + 12) +
f(5 + 2.12) + …….. + f(5 + 250.12)
= f(5) + f(5) + f(5) …….. upto 251 times
⇒ 251 f(5) = 251 × 8 = 2008
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