Question

using difference table find the value of (Δ)2y given the values of (x, y) as (1,5),(2,14),(3,21)?​

Answer 1

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Answer 2

The value of Δ²y is -2.

Given:

values for x = 1, 2,3

corresponding values of y = 5, 14, 21

To Find:

Δ²y for the given values

Solution:

We shall solve this problem using forward difference method

In forward difference method we keep x and y column and column of Δy and Δ²y

here value of $x_{0}=1$ ,   $x_{1}=2, x_{2}=3$

Similarly $y_{0}=5, y_{1}=14, y_{2}=21$

forward difference method states to take difference of $y_{n+1} - y{n}$ this is the first difference denoted by Δy

Second differences are differences of first differences of  Δ ($y_{n+1}-y_{n}$) = Δ $y_{n+1}$ - Δ $y_{n}$ this is the second differences are denoted by Δ²y

In tabular form we can write it as

x      y      Δy    Δ²y

1      5

               -9

2     14              -2

               -7

3     21

So, the value of Δ²y is -2.

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