Question

2, 4, 6, 8, 10 is a sequence.
Find the algebraic expression in this sequence.​

Answer 1

Answer:

This is an arithmetic sequence since there is a common difference between each term. In this case, adding

2

to the previous term in the sequence gives the next term. In other words,

Arithmetic Sequence:

d=2

Answer 2

Question:

2, 4, 6, 8, 10 is a sequence.

Find the algebraic expression in this sequence.

To find:

★ To find the algebraic expression.

Answer:

$The \:algebraic \:expression\: is\: \underline{\:\sf\pink{ \bold{2n}}\:}$

Given:

★ A sequence is given, it's in A.P.

$2,4,6,8,10$

The given sequence is an A.P.

Step-by-step explanation:

$2,4,6,8,10$

The given sequence is an A.P.

$First \: term \: \underline{(a) = 2}$

$Common \: difference \underline{(d) = t _{2} - t _{1}}$

$\star \: t _{1} = 2$

$\star \: t _{2} = 4$

$\hookrightarrow d = 4 - 2$

$\hookrightarrow \boxed{d = 2}$

$No. \: of \: terms \: = \bold{ n \: is \: not \: given}$

Now finding the algebraic expression,

Algebraic expression is nothing but finding the ${n}^{th}\:term$

${n}^{th} \: term : -$

$\boxed{t _{n} = a + (n - 1)d}$

Now substituting the values,

$\implies t _{n} = 2 + (n - 1)2$

$\implies t _{n} = \not{2} + 2n - \not{2}$

$\implies \boxed{t _{n} = 2n}$

$\therefore$The algebraic expression is $\underline{\: \bold{2n}\:}$

More information:

★ Arithmetic Progression :

In a sequence the difference between two consecutive terms are equal it is called Arithmetic Progression.

★ No. of terms :

$n=\dfrac{l-a}{d}+1$

★ Sum of terms :

$S_{n}=\dfrac{n}{2}\big[2a+(n-1)d\big]$

⚠️Note⚠️

${n}^{th}\: term\: can\: also \:be\: written\:as\:\bold{t_{n}\: or \:a_{n}}$