SOLUTION: The number of terms in a Arithmetic progression is even,the sum of the odd terms is 24 and sum of the even terms is 30 and if the last term exceeds the first term by 21/2,find the

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Question 51319: The number of terms in a Arithmetic progression is even,the sum of the odd terms is 24 and sum of the even terms is 30 and if the last term exceeds the first term by 21/2,find the numbers
Answer by venugopalramana(3286) (Show Source):
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The number of terms in a Arithmetic progression is even,the sum of the odd terms is 24 and sum of the even terms is 30 and if the last term exceeds the first term by 21/2,find the numbers
LET FIRST TERM =A
LAST TERM = A+21/2=A+10.5
LET NUMBER OF TERMS =2N
A+10.5=A+(2N-1)D
D=10.5/(2N-1)...2D=21/(2N-1)
SUM OF ODD TERMS = A+(A+2D)+(A+4D)+..............N TERMS
=(N/2)[2A+(N-1)2D]=(N/2)[2A+(N-1)*21/(2N-1)]=24...........1
SUM OF EVEN TERMS = (A+D)+(A+3D)+......N TERMS
=(N/2)[2A+21/(2N-1) + (N-1)21/(2N-1)]=30.............2
EQN.2-EQN.1
(N/2)[21/(2N-1)]=6
21N=12(2N-1)=24N-12
3N=12
N=4
D=10.5/(2*4-1)=1.5
A=1.5