Question

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

Answer 1

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,

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

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

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

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

Answer 2

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.