Question

6th term of an AP is zero. Find the relation between 31st term and 11th term.​

Answer 1

Answer:

5 times the 11th term

Step-by-step explanation:

a+5d = 0

31st term = a+30d = -5d+30d = 25d

11th term = a+10d = -5d+10d = 5d

Relation = 25d/5d = 5

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Answer 2

31st term is 5 times the 11th term.

Given :

6th term of an AP is zero

To find :

The relation between 31st term and 11th term.

Concept :

If in an arithmetic progression

First term = a

Common difference = d

Then nth term of the AP

= a + ( n - 1 )d

Solution :

Step 1 of 3 :

Express first term in terms of common difference

Let first term = a and common difference = d

6th term

= a + (6 - 1)d

= a + 5d

By the given condition

a + 5d = 0

⇒ a = - 5d

Step 2 of 3 :

Calculate 31st term and 11th term.

31st term

= a + (31 - 1)d

= a + 30d

= - 5d + 30d

= 25d

11th term

= a + (11 - 1)d

= a + 10d

= - 5d + 10d

= 5d

Step 3 of 3 :

Find the relation between 31st term and 11th term.

31st term = 25d

11th term = 5d

Thus we observe that , 31st term = 5 × 11th term.

Hence 31st term is 5 times the 11th term.

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