Question

if nth term of a sequence is 2n^2 +1 = 3 find the sequence .is this sequence in A.p ?

Answer 1

solution


given :-
$tn = {2n}^{2} + 1$
putting n= 1

t1 = 2*1 ^2 + 1 = 3


putting n= 2

t2 = 2*2 ^2 +1 = 9

putting n= 3

t3 = 2*3^2 + 1= 19

putting n = 4

t4 = 2*4^2+ 1 = 33

... .... .... .....

... .... ..... ......


and so on

since given sequence is 3,9,19,33

bold\{second part}

T{n-1} = 2( n-1) ^2 +1

from 1 and 2eq

t{n} -t{n-1} = 2n^2 +1 - { 2( n-1} ^2 +1)


= 2n^2 +1 - { 2( n^2 -2n + 1) +1}


= 4n- 2 .


which is not independent of n , I. e which is not a constant , hence given sequence is not an ap.


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