Prove that nth term of an AP can't be n^2+n+1.
Answers
Solution :-
Now we know that what is A.P
A.P is series in which the difference between the two consecutive terms is constant.
Now as given expression for nth term
= n² + n + 1
So
(n-1) th term
= (n-1)² +(n-1) + 1
= n² - 2n + 1 + n - 1 + 1
= n² -n + 1
Now we will find out the common difference :-
nth term - (n-1)th term
→ n² + n + 1 - ( n² -n + 1 )
→ n² + n + 1 - n² + n - 1
→n² - n² + n + n + 1 - 1
→ 2n
Now as d is not a constant value i.e it is dependent upon a variable quantity "n"
So n² + n + 1 cannot be nth term of an AP
Answer:
Solution :-
Now we know that what is A.P
A.P is series in which the difference between the two consecutive terms is constant.
Now as given expression for nth term
= n² + n + 1
So
(n-1) th term
= (n-1)² +(n-1) + 1
= n² - 2n + 1 + n - 1 + 1
= n² -n + 1
Now we will find out the common difference :-
nth term - (n-1)th term
→ n² + n + 1 - ( n² -n + 1 )
→ n² + n + 1 - n² + n - 1
→n² - n² + n + n + 1 - 1
→ 2n
Now as d is not a constant value i.e it is dependent upon a variable quantity "n"
So n² + n + 1 cannot be nth term of an AP
Step-by-step explanation: