Arithmetic progression

joyseychow · **Posted:** Thu Aug 06, 2009 11:05 pm


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The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?
A. 300
B. 120
C. 150
D. 170
E. 270

bhushan252 · **Posted:** Thu Aug 06, 2009 11:35 pm

OA C

Sum of the AP = avg of AP x no of terms
Avg of the AP can be found by addition of (first term + last term) /2 or (second +second last term)/2 or (third +third last term)/2.... try this out its a property of any AP....here as we need to find sum of first 15 terms...let us assume AP of 15 terms....

for this AP..going by above logic..... (1st +15th term) = (4th + 12 th term) = 20
hence Avg of AP = 10

Sum of the AP = 10 x 15 = 150 :-D

age · **Posted:** Thu Aug 06, 2009 11:54 pm

IMO C...

n th term of A.P. is given by a+(n-1)d
4 th term = a+3d
12 th term = a+11d

Given a+3d+a+11d=20 --> 2a+14d=20 --> a+7d = 10

Sum of n term of A.P = n/2[2a+(n-1)d]
subsitiuing n = 15 ...we get 15/2[ 2a + 14d] = 15 [a+7d] = 15*10 = 150...

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Arithmetic progression

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