Question

first term of an arithmetic sequence is f, common difference D what is its fifth term​

Answer 1

Answer:

Fifth term = f+4D

hope this helps u

Answer 2

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 =

Putting all values :-

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

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

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

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

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

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

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

$[2a+(n−1)d]$

Where,

a denotes first term

n denotes number of terms

d denotes common difference

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