Question

In an AP The 11th and 13th term of an AP are 35 and 41 respectively , its common difference is ?

Answer 1

Answer:

3

Step-by-step explanation:

a11= 35

a13=41

ACC. to questions

by elimination method

35=a+10d

41=a+12d

-6= 0-2d (d=common difference)

-2d=-6

d=-6/-2=3

d=3

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Answer 2

Answer:

The common difference is 3.

Step-by-step explanation:

Given: $a_{11}$ = 35 and $a_{13}$ = 41

To find: commen difference, d

Solution:

We know, The general formula for arithmetic expression is

$a_{n} = a + (n - 1)d$

were, $a_{n}$ = nth term

a = 1st term

d = common difference

∴ Putting the value in above expression

Case 1: For 11th term

⇒ $a_{11} = a + (11 - 1)d$

⇒ $a_{11} = a + 10d$

∴ 35 = a + 10d  ---------------(i)

Case 2: For 13th term

⇒ $a_{13} = a + (13 - 1)d$

⇒ $a_{13} = a + 12d$

∴ 41 = a + 12d  ---------------(ii)

Now, Subtracting equation (i) from (ii)

we get,

41 - 35 = (a + 12d) - (a+ 10d)

=> 6 = a + 12d - a - 10d

=> 6 = 2d

∴ d = 3

Hence, the common difference is 3. Ans.

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