Hi,

Given $ u_1=1, u_1+u_3=5.41, u_4+u_5+u_6=18.47, u_7+u_8+u_9+u_{10}+u_{11}+u_{12}=90.36 $

Find the values of $ u_x $ for x=1,2,...,12.

Solution:-

I calculated $ S_3 =u_1+u_2+u_3=5.41+u_2, S_6=u_1+u_2+....+u_6=23.88+u_2, S_{12}=u_1+....+u_{12}=114.24+u_2 $

as 1,3,6,12 are at unequal intervals, I want to use Newton's divided difference interpolation formula.

for calculating $ u_2 $ shall I use $ (E-1)^2 u_x=0 $ when x=1

Problem solving hint is needed.