Question

2nd term 5
5th term 2
write the first five term​

Answer 1

Answer:

6 , 5 , 4 , 3 and 2

Step-by-step explanation:

 Let the first term be a and common difference be d.

In APs nth term is given by a + ( n - 1 )d, where a and d have their usual meaning.

  So,

    2nd term = 5

 ⇒ a + ( 2 - 1 )d = 5

 ⇒ a + d = 5

 ⇒ a = 5 - d   ...( 1 )

     5th term = 2

 ⇒ a + ( 5 - 1 )d = 2

 ⇒ a + 4d = 2

                   a = 5 - d

 ⇒ 5 - d + 4d = 2  

 ⇒ 3d = - 3

 ⇒ d = - 1

         Hence,

             a = 5 - d

                = 5 - ( - 1 )

                = 5 + 1

                = 6

Hence,  

  1st = 6

2nd = 6 - 1 = 5

3rd = 6 - 2 = 4

4th = 6 - 3 = 3

5th = 6 - 2 = 2

Answer 2

$\rule{300}2$

$\huge\bold{\mathtt{QUESTION}}$

➡ Second term of an AP is 5 and fifth term is 2 . Find the first five terms of the given AP .

$\rule{300}2$

$\huge\bold{\mathtt{SOLUTION}}$

☯ The terms in an AP is given by → $\sf a + (n-1)d$

Where , n = no. of term

▶ACCORDING TO THE QUESTION -

✳ When n = 2

$\sf \:\:\:\:\:\:\:\:\:\:\:\:a\:+\:(2-1)d\:=\:5$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:a\:+\:d\:=\:5$

Here , a = 5 - d ----------- ( EQ-1 )

✳ When n = 5

$\sf \:\:\:\:\:\:\:\:\:\:\:\:a\:+\:(5-1)d\:=\:2$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:a\:+\:4d\:=\:2$

Put value of ( a ) from equation 1

$\sf \:\:\:\:\:\:\:\:\:\:\:\:5\:-d\:+\:4d\:=\:2$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:3d\:=\:2\:-\:5$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:{\underline{d\:=\:-1}}$

Now , a - d = 5 (eq 1)

↪a + ( - 1 ) = 5

↪ a - 1 = 5

↪ a = 5 + 1

↪ a = 6

☯ First term is 6

☯ Second term is 5

☯ Third term is 4 [ 6 + 2(-1) = 4 ]

☯ Fourth term is 3 [ 6 + 3(-1) = 3 ]

☯ Fifth term is 2

$\rule{300}2$