Home
Class 12
MATHS
Show that the the sequence defined by ...

Show that the the sequence defined by ` T_(n) = 3n^(2) +2 ` is not an AP.

Text Solution

Verified by Experts

We have, `t_n=3n^(2)+2`
On replacing n by `(n-1),` we get
`t_(n-1)=3(n-1)^(2)+2`
`implies t_(n-1)=3n^(2)-6n+5`
`therefore t_n-t_(n-1)=(3n^(2)+2)-(3n^(2)-6n+5)`
`" "=6n-3`
Clearly, `t_n-t_(n-1)` is not independent of n and therefore it is not constant. So, the given sequence is not an AP.
Promotional Banner

Similar Questions

Explore conceptually related problems

Show that the sequence t_(n) defined by t_(n)=2*3^(n)+1 is not a GP.

Show that the sequence t_(n) defined by t_(n)=5n+4 is AP, also find its common difference.

Show that the sequence t_(n) defined by t_(n)=(2^(2n-1))/(3) for all values of n in N is a GP. Also, find its common ratio.

What is the 20^(th) term of the sequence defined by a_(n)= (n-1) (2-n) (3+n) ?

Show that the sum of (m + n)^(th) and (m – n)^(th) terms of an A.P. is equal to twice the m^(th) term.

Show that a_(1), a_(2) ,……, a_(n) …. Form an AP where a_(n) is defined as below: (i) a_(n) = 3 + 4n , (ii) a_(n) = 9-5n Also find the sum of the first 15 terms in each case.

The Fibonacci sequence is defined by 1=a_(1)=a_(2) and a_n =a_(n-1)+a_(n-2) , n gt 2 Find (a_(n+1))/a_n for n = 1, 2, 3, 4, 5

Write the first three terms in each of the following sequences defined by the following a_(n)= (n-3)/(4)