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Q.1. The number of terms of an A.P. is even;the sum of the odd terms is 24,of the even terms is 30,and the last term excceds the first term by1012,find the number of terms and the sries.
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2 Answers
23a = first term , d = common difference
S= 54 = n(2a+(n-1)d)/2......(1)
tn=a + 10.5
so a + (n-1)d = a + 10 . 5
so d = nd - 10.5 .........(2)
Sodd=n(a+tn-1)/4 = 24
Seven=n(t2+tn)/4=30
divide S odd by S even
5a + 5tn-1=4t2+4tn
5a+5a+5(n-2)d = 4a+4d + 4a+4(n-1)d
2a+nd= 10d
put dis in 1
so 54 x 2 = n (9d )
so nd = 12 put in 2
so d = 1.5
so n = 8
so a = 3/2