Question

arithmetic progression ka question h please solve only if you know for solving it correctly I will give you 5 star rating heart (thanks) and mark as brainliest ​.

Answer 1

The algebraic expression of the sequence is,

$\displaystyle\longrightarrow\sf{a_n=2n^2+1}$

Let's find first three terms of the sequence.

$\displaystyle\longrightarrow\sf{a_1=2(1)^2+1}$

$\displaystyle\longrightarrow\sf{a_1=3\quad\quad\dots (1)}$

And,

$\displaystyle\longrightarrow\sf{a_2=2(2)^2+1}$

$\displaystyle\longrightarrow\sf{a_2=9\quad\quad\dots (2)}$

And,

$\displaystyle\longrightarrow\sf{a_3=2(3)^2+1}$

$\displaystyle\longrightarrow\sf{a_3=19\quad \quad\dots(3)}$

Subtracting (1) from (2),

$\displaystyle\longrightarrow\sf{a_2-a_1=9-3}$

$\displaystyle\longrightarrow\sf{a_2-a_1=6\quad\quad\dots (4)}$

Subtracting (2) from (3),

$\displaystyle\longrightarrow\sf{a_3-a_2=19-9}$

$\displaystyle\longrightarrow\sf{a_3-a_2=10\quad\quad\dots (5)}$

Comparing (4) and (5),

$\displaystyle\longrightarrow \sf{a_2-a_1\neq a_3-a_2}$

The differences between consecutive terms are not equal, so the sequence does not have common difference.

Hence the sequence is not an AP. Because AP is a sequence in which consecutive terms differ by the same number.

Answer 2

$\rm Algebraic \ expression \ of \ the \ sequence \ : \ \bf a_{n}=2n^{2} +1\\\\\rm Let \ us \ find \ first \ four \ terms \ of \ the \ sequence \ .\\\\\rm\longrightarrow a_{1}=2\times 1^{2} +1 \\\\\rm\longrightarrow a_{1}=3\\\\\\\rm\longrightarrow a_{2}=2\times 2^{2} +1\\\\\rm\longrightarrow a_{2}=9\\\\\\\rm\longrightarrow a_{3}=2\times3^{2} +1\\\\\rm\longrightarrow a_{3}=19\\\\\\\rm\longrightarrow a_{4}=2\times 4^{2}+1\\\\\rm\longrightarrow a_{4}=33$

$\rm\Longrightarrow a_{2}-a_{1}=9-3=6\\\\\rm\Longrightarrow a_{3}-a_{2}=19-9=10\\\\\rm\Longrightarrow a_{4}-a_{3}=33-19=14\\\\\\\rm \bf a_{2}-a_{1}\neq a_{3}-a_{2}\neq a_{4}-a_{3}$

∴ HENCE PROVED

In an Arithmetic sequence difference between two  consecutive terms are the same .

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