#Algebra-4

An arithmetic progression consists of an even number of terms. The sum of its odd terms is 50 whereas the sum of its even terms is 56. Find the number of terms in the series if the last term of the series exceeds the first term by 11.25.

Solution-
Let the total number of terms = 2n
Sum of odd terms = 50
a1 + a3 + a5  + a7 + ... + a(2n-1) = 50 - ------------(1)
Sum of even terms = 56
a2 + a4 + a6 + a8 + ....  +a(2n) = 56 -------------(2)

Subtract eqn (1) from (2),
(a2 - a1) + (a4 - a3) + ...... + (a(2n) - a(2n-1) = 6
=>d + d + .....................+ d = 6
=>n*d = 6----------(3)
Now, a1 + (2n-1)d - a1 = 11.25
=> (2n-1)d = 11.25--------(4)
eqn (3)/(4),
n/(2n-1) = 6/(11.25)
=> n = 8
Number of terms = 2n = 2*8 = 16 ANS

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