Question

U0+u8=1.9243,u1+u7=1.9590,u2+u0=1.9823,u3+u5=1.9956 find u4

Answer 1

The answer is given in the picture attachment.

Answer 2

Given:

U0+u8 =1.9243,

u1+u7 = 1.9590,

u2+u0 =1.9823,

u3+u5=1.9956

To Find:

Value of u4

Solution:

Taking the seventh difference to be constant -

Δ8uo = 0 and

Δ8uo = ( E - 1) 8u0

u8 - 8c1u7 + 8c2u6 + 8c3u5 + 8c4u4 - 8c5u3 + 8c6u2 - 8c7u1 + 8c8u0

u0+u8 - 8(u1+u7) + 28(u2+u6) - 56(u3+u5) + 70u4

= 1.9243 - 8(1.9590) + 28(1.9823) - 56(1.9956) + 70u4

= 1.9243 - 15.6720 + 55.5044 - 111.7536 + 70u4

Δ8u0 = 70u4 - 69.9969

Therefore,

u4 = 69.9969/70

= 0.9999

Answer: The value of u4 is 0.9999