Math, asked by sivadassreevalsam, 9 months ago

The term of an arithmetic sequence 3-5n. write first term and common difference​

Answers

Answered by SarcasticL0ve
10

Given:-

  •  \sf{ n^{th} \; term \; of \; an \; arithmetic \; sequence \; is \; 3-5n.}

To find:-

  • First term (a)

  • Common difference (d)

Solution:-

\implies \sf{ n^{th} \; term = 3-5n}

  • First term (  \sf a_1 )

Put value of n = 1

\implies \sf{ \sf a_1 = 3-5(1)}

\implies \sf{ \sf a_1 = -2}

  • Second term (  \sf a_2 )

Put value of n = 2

\implies \sf{ \sf a_1 = 3-5(2)}

\implies \sf{ \sf a_2 = -7}

  • Third term (  \sf a_3 )

★ Put value of n = 3

\implies \sf{ \sf a_1 = 3-5(3)}

\implies \sf{ \sf a_2 = -12}

So, the required AP is  \sf{ \bigg[ -2, -7, -12,....... \sf a_n \bigg]}

Now,

\bold{\underline{\boxed{\sf{\pink{\dag \; First \; term ( \sf a_1 ) = -2}}}}}

and,

 \sf{Common \; difference (d) = \sf a_1 - \sf a_2 }

 \sf{ \sf a_1 - \sf a_2 = -2 -(-7) = 5 }

\bold{\underline{\boxed{\sf{\pink{\dag \; Common \; difference (d) =  5}}}}}

\underline {\rule{261}{2}}

Answered by Anonymous
1

AnSwer:-

The first term is -2 and common difference is -5.

Given:

In arithmetic sequence,

tn=3-5n

To Find:

First term and common difference.

SoLution:

•tn=3-5n

Let n be 1,

t1=3-5(1)

=>t1=3-5

=>t1= -2

Let n be 2,

t2=3-5(2)

=>t2=3-10

=>t2= -7

Common difference (d)=t2-t1

t2-t1= -7-(-5)

t2-t1= -2

The first term is -2 and common difference is -5.

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