Question

If a1,
a
2, a
3, ........ , an and b
1, b
2, b
3, ........ ,bn are two Arithmetic Progressions.
Is a1 + b
1, a2 + b
2, ........, a
n + bn an Arithmetic Progression? Why/ Why not?

Answer 1

a1,  a2,  a3, ....  an  are in AP  :  let the common difference be  d
b1, b2,  b3  ....  bn  are in AP :  let the common difference be  e.


a1 + b1
a2 + b2 = a1 + b1 + (d + e)
a3 + b3 = a1 + b1 + 2 (d + e)
an + bn = a1 + b1 + (n-1) d + (n-1)e = (a1+b1) + (n-1) (d+e)

So  an + bn  is an AP  with first term  a1 + b1  and  common difference = d+e.