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23 Nov 2021, 09:45
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C
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Difficulty:
45%
(medium)
Question Stats:
74% (02:36) correct
26%
(02:42)
wrong
based on 240
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The function f(x) is defined as \(f(x+1) = f(x) + 5\). If \(f(0) = 37\), what is the sum of \(f(3) + f(4) +.... f(10)\)?
A. 476
B. 516
C. 556
D. 596
E. 636
A. 476
B. 516
C. 556
D. 596
E. 636
23 Nov 2021, 10:02
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Easy, function is arithmetic progressive series with diff(d) of 5. With a= f(3)= f(0)+ 5*3= 52. Sum of a.p. = n/2[2*a + (n-1)*d] with n = 8 (10-3+1). Result is 556.
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24 Jun 2024, 04:57
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↧↧↧ Detailed Video Solution to the Problem ↧↧↧
f(x+1) = f(x) + 5 and f(0) = 37 and we need to find the value of f(3) + f(4) +.... f(10)
f(1) = f(0+1) = f(0) + 5 = 37 + 5 = 42
f(2) = f(1) + 5 = 42 + 5 = 47
f(3) = f(2) + 5 = 47 + 5 = 52
f(4) = f(3) + 5 = f(3+1)
f(5) = f(4) + 5 = f(3) + 5*2 = f(3+2)
.
.
.
f(10) = f(3+7) = f(3) + 5*7
=> f(3) + f(4) +.... f(10) = f(3 ) + f(3) + 5*1 + f(3) + 5*2 + .... f(3) + 5*7 = 8*f(3) + 5 * ( 1+ 2+ ...7)
= 8*52 + 5 * \(\frac{7*8}{2}\) = 416 + 28*5 = 416 + 140 = 556
So, Answer will be C
Hope it helps!
Watch the following video to MASTER Functions and Custom Characters
f(x+1) = f(x) + 5 and f(0) = 37 and we need to find the value of f(3) + f(4) +.... f(10)
f(1) = f(0+1) = f(0) + 5 = 37 + 5 = 42
f(2) = f(1) + 5 = 42 + 5 = 47
f(3) = f(2) + 5 = 47 + 5 = 52
f(4) = f(3) + 5 = f(3+1)
f(5) = f(4) + 5 = f(3) + 5*2 = f(3+2)
.
.
.
f(10) = f(3+7) = f(3) + 5*7
=> f(3) + f(4) +.... f(10) = f(3 ) + f(3) + 5*1 + f(3) + 5*2 + .... f(3) + 5*7 = 8*f(3) + 5 * ( 1+ 2+ ...7)
= 8*52 + 5 * \(\frac{7*8}{2}\) = 416 + 28*5 = 416 + 140 = 556
So, Answer will be C
Hope it helps!
Watch the following video to MASTER Functions and Custom Characters
