Question

The 4th term of an Ap is 11. The sum of the 5th and 7 th terms of this Ap is 34. find its common difference

Answer 1

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Given :-

• The 4th term of an Ap is 11.
• The sum of the 5th and 7 th terms of this Ap is 34

To find :-

• Common difference

Sóĺúťíóń :-

We will consider here seven consecutive terms in an AP.

Let the terms be :-

First term :- a - d

Second term :- a

Third term :- a + d

Fourth term :- a + 2d

Fifth term :- a + 3d

Sixth term :- a + 4d

Seventh term :- a + 5d

Value of fourth term is 11. Representing this mathematically using the terms we will get our first equation.

a + 2d = 11 -----> 1

As per the second condition,

• The sum of the 5th and 7 th terms of this Ap is 34.

Representing it mathematically and solving it further, we will get the second equation,

a + 3d + a + 5d = 34

2a + 8d = 34 -----> 2

Multiply equation 1 by 2,

2 × a + 2 × 2d = 2 × 11

2a + 4d = 22 ----> 3

Solve equations 3 and 2 simultaneously by elimination method.

Subtract equation 3 from 2,

....+ 2a + 4d = + 22

- (+2a + 8d = + 34 )

------------------------------

- 4d = - 12

d = $\bf\large\frac{-12}{-4}$

d = $\bf\large\frac{12}{4}$

d = 3

Common difference = 3

Answer 2

Step-by-step explanation:

Answer:-

The common difference is

3