Question

Show that the sequence defined by an=2n²+3 is not an AP​

Answer 1

Answer:

hey frnd here is your answer

Step-by-step explanation:

• Term=2n²+3

• by putting n=1 we get 1st Term as 5.
• by putting n=2 we get 2nd Term as 11
• by putting n=3 we get 3rd Term as 21

• so the three terms are 5,11,21

• so we can clearly say that 5,11,21 are not in Ap.

• This numbers are not in AP because here there is 2b=a+c is not followed by this three numbers.

I hope you understand my answer

thnx for asking

plzz mark as brainlist...

Answer 2

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies a_{n} = 2 {n}^{2} + 3 \\ \\ \red{\underline \bold{To \: Show:}} \\ \tt: \implies a_{n} \: not \: form \: an \:A.P$

• According to given question :

$\tt \circ \: a_{n} = {2n}^{2} + 3 \\ \\ \tt\because \: n = 1,2,3,4,... \\ \\ \bold{As \: we \: know \: that(n = 1)} \\ \tt: \implies a_{1} = 2 \times {1}^{2} + 3 \\ \\ \tt: \implies a_{1} =2 + 3 \\ \\ \green{\tt: \implies a_{1} =5} \\ \\ \bold{For \: n = 2} \\ \tt: \implies a_{2} = {2 \times 2}^{2} + 3 \\ \\ \tt: \implies a_{2} =8+ 3 \\ \\ \green{\tt: \implies a_{2} =11} \\ \\ \bold{For \: n = 3} \\ \tt: \implies a_{3} =2 \times {3}^{2} + 3 \\ \\ \tt: \implies a_{3} =2 \times 9 + 3 \\ \\ \tt: \implies a_{3} =18 + 3 \\ \\ \green{\tt: \implies a_{3} =21} \\ \\ \bold{For \: a_{n} \: in \: A.P} \\ \tt: \implies a_{3} - a_{2}=a_{2} - a_{1} \\ \\ \tt: \implies 21 - 11 = 11 - 5 \\ \\ \tt: \implies 10 \cancel{=} 6 \\ \\ \: \: \: \: \huge{\red{\bold{proved } }}$