Question

Satement 1 If the nth termn of a series is `2n^(3)+3n^(2)-4`, then the second order differences must be an AP.
Statement 2 If nth term of a series is a polynomial of degree m, then mth order differences of series are constant.
A. Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1
B. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1
C. Statement 1 is true, Statement 2 is false
D. Statement 1 is false, Statement 2 is true

Answer 1

Correct Answer - A
`:.T_(n)=2n^(3)+3n^(2)-4`
Sequence is `1,24,77,172,321,"……"`
First order difference `23,53,95,149,"…."`
Second order difference `30,42,54,"…."`
which are in AP.
`:.` Statement 1 is true.
`:. T_(n)` is of three degree and third order difference will be constant.
Statement 2 is true, which is correct esplanation for Statement 1.