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.