Question

Find the algebraic expression of the AP 11,22,33​

Answer 1

ANSWER:

Given:

• AP = 11, 22, 33...

To Find:

• Algebraic Expression of the AP

Solution:

We are given an AP 11, 22, 33...

The Algebraic Expression of an AP is the formula for its general term.

So, we need to find the General term of this AP.

⇒ AP = 11, 22, 33..

• First term(a) = 11
• Common difference (d) = 22 - 11 = 33 - 22 = 11

We know that,

⇒ T_n = a + (n - 1)d

So,

⇒ T_n = 11 + (n - 1)11

⇒ T_n = 11 + 11n - 11

Hence,

⇒ T_n = 11n

Hence, the general term of the AP is 11n.

Therefore, the Algebraic Expression of the AP is 11n.

Answer 2

Hint:

If $a_{1},a_{2},a_{3},...,a_{n}$ be an Arithmetic Progression with $d$ being the common difference, then we can have

$\quad a_{n}=a_{1}+(n-1)d$

Step-by-step explanation:

Given, Arithmetic Progression $11,22,33,...$

Here the first term, $a_{1}=11$

and the common difference, $d=a_{2}-a_{1}=22-11=11$

Hence the nth term,

$\quad a_{n}=a_{1}+(n-1)d$

$\Rightarrow a_{n}=11+(n-1)\times 11$

$\Rightarrow a_{n}=11+11n-11$

$\Rightarrow a_{n}=11n$

Here this nth term is the general term for the given progression.

Final answer: $11n$

The algebraic expression of the A.P. $11,22,33,...$ is $11n$.

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