Question

The first term of an arithmetic sequence is 3 and the common difference is 2.What is its 10th term?​

Answer 1

Given :-

• First term of an AP = 3
• Common difference (d) = 2

To Find :-

• 10th term of AP?

Solution :-

Using formula of nth term of an AP. We clearly know that,

$\hookrightarrow\:{\large{\boxed{\sf{a_{n} = a + (n - 1)d}}}}$

Where,

• a denotes first term
• n denotes number of terms
• d denotes common difference

We have,

• a = 3
• n = 10
• d = 2

Putting all values :-

$\\ :\implies\:\sf a_{10} = 3 + (10 - 1)2$

$\\ :\implies\:\sf a_{10} = 3 + (9\:\times\:2)$

$\\ :\implies\:\sf a_{10} = 3 + 18$

$\\ \purple{:\implies}\:{\large{\underline{\boxed{\bf{\blue{a_{10}} \pink{=} \red{21}}}}}}$

Hence, 10th term of an AP is 21.

Extra Information :-

$\spadesuit$ Some definitions,

• AP

An arithmetic progression is a list of numbers in which each term is obtained by adding fixed number to preceding term except the first term.

• Common difference

The fixed number which is added to preceding term to get next term is called common difference. Note :: Common difference can be zero, positive or negative.

$\spadesuit$ Formulas related to AP,

‣ Formula of nth tern of an AP

$\hookrightarrow\:{\large{\boxed{\sf{a_{n} = a + (n - 1)d}}}}$

‣ Formula of sum of nth term of an AP

$\hookrightarrow\:{\large{\boxed{\sf{S_{n} = \dfrac{n}{2}\Big[2a + (n - 1)d\Big]}}}}$

Where,

• a denotes first term
• n denotes number of terms
• d denotes common difference

Related Question :

• Find the 16th term of an A.P., whose 1st term is 15 and common difference is -2.

Answer :

• brainly.in/question/45635782

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Answer 2

Given :

• First term of an arithmetic sequence is 3 .
• Common difference is 2 .

To Find :

• 10th term

Solution :

$\longmapsto\tt{First\:term\:(a)=3}$

$\longmapsto\tt{Common\:difference\:(d)=2}$

$\longmapsto\tt{No\:of\:terms\:(n)=10}$

Using Formula :

$\longmapsto\tt\boxed{{a}_{n}=a+(n-1)\times{d}}$

Putting Values :

$\longmapsto\tt{{a}_{10}=3+(10-1)\times{2}}$

$\longmapsto\tt{{a}_{10}=3+(9)\times{2}}$

$\longmapsto\tt{{a}_{10}=3+18}$

$\longmapsto\tt\bf{{a}_{10}=21}$

So , The 10th term of the sequence is 21 .

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• $\tt{{a}_{n}=a+(n-1)\times{d}}$
• $\tt{{s}_{n}=\dfrac{n}{2}[2a+(n-1)\times{d}}$

• $\tt{{s}_{n}=\dfrac{n}{2}\:[a+l]}$

Here :

• a = first term
• d = common difference
• n = number of terms
• l = last term

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