Question

What is the common difference of an ap in which 27th term and 7th term when subtracted gives 84

Answer 1

T 27 - T 7 = 84

a + 26d - ( a + 6d ) = 84

a + 26d - a - 6d = 84

20d = 84

d = 84 / 20

d= 21 / 5

hence , the common difference d
= 21 / 5

Answer 2

Answer:

4.2 is the required common difference of the A.P

Step-by-step explanation:

Explanation:

Given ,  $a_{27} - a_{7}$ = 84

And we know that  nth term of an A.P ,

$a_n$ = a + (n-1)d

Where , a is the first term , n is the number of term and d is the common difference .

Step 1:

So according to the given information we have ,

$a_{27} - a_{7}$ = 84 .........(i)

But we have ,

$a_{27} = a + (27 - 1)d$ = a + 26d

and , $a_7 =a+ ( 7 - 1) d$ = a + 6d

Now put the value in (i) we get ,

(a+ 26d ) - (a +6d) = 84

⇒20d = 84                          [a and a are cancel out ]

⇒ d = $\frac{84}{20}$ = 4.2

Final answer:

Hence , the common difference of the A.P is 4.2 .

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