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1. Find the arithematic progression whose third term is 16 and seventh term exceeds its fifth term by 12?
2. If an A.P consists of n terms with first term a and nth term l show that the sum of the mth term from the beginning and the mth term from the end is (a+l)?
1. nth term can be given by a+(n-1)d
so, when n=3, a+2d=16.......................(1)
also when n=5 and n=7,
a+6d-a-4d=12
so 2d=12
d=6
now, from (1)
a=4
so the AP is 4, 10, 16, .....
2. mth term from beginning is a + (m-1)d
mth term from the end is l - (m-1) d
a + (m-1)d + l - (m-1) d ( according to given condition )
= a+(m-1)d + l - (m-1)d
= a+ l
= hence proved.
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