Question

+ If the first term (a) is 6 and the sixth term (t) is 31, find (i) the common
difference (ii) the fifth term (iii) the seventh term of the sequence.​

Answer 1

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

Given,

a=6 and 6th term=31

Now,

6th term=31

→a+5d=31

→6+5d=31

→5d=25

→d=5

Here,(a,d)=(6,5)

To find: 5th term and 7th term

5th term:

a+4d

=6+4(5)

=20+6

=26

7th term:

a+6d

=6+6(5)

=36

Answer 2

Answer:

Fifth Term ⇒ 26

Seventh Term ⇒ 36

Step-by-step explanation:

Assuming p and q as the first term & common difference of the both respectively ;

Given that ,

⇒ p = 6 and 6th term = 31

As ,

⇒ 6th Term = 31

⇒ p + 5q = 31

⇒ 6 + 5q = 31

⇒ 5q = 31 - 6 = 25

⇒ q = 25/5 = 5

So here , ( p , q ) ⇒ ( 6 , 5 )

Now ,

Finding the 5th & 7th term ;

Fifth Term ;

⇒ p + 4q

⇒ 6 + 4(5)

⇒ 6 + 20

⇒ 26

Seventh Term ;

⇒ p + 6q

⇒ 6 + 6(5)

⇒ 6 + 30

⇒ 36