Question

The common difference of an AP whose 8th term from the last is 30 and last term is 65, is

Answer 1

Answer:

the common difference of an ap whose 8 term from last is 30 and last term is 65 is​

let the AP : a, a+d, a+2d ......

to calculate the nth term of an AP from last, we need to write it in reverse order

New AP : 65, 65+d, 65+2d

Let the common difference be D

D= a2-a1

D= (65+d)-65

D= 65+d-65

D= d

Now,

the 8th term =30

a1+(8-1)D = 30

65+7d =30  

7d=30-65

d= -35/7

d= -5

Explanation:

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Answer 2

The common difference between an AP whose 8th term from the last is 30 and the last term is 65,

Now,

let the AP = a, (a+d), (a+2d), .....................

According to the question;

let new AP = 65 , (65 +d), (65+ 2d),...................

let the common difference be D

D = $a_{1} - a_{2}$

D= (65 +d) - 65

D= 65 + d - 65

D = d

now,

8th term = 30

now, according to 8th term;

$a_{1} + ( 8 - 1 ) D = 30\\65+ 7d = 30\\7d= 30 - 65\\7d = - 35\\d = -5$

The common difference between an AP whose 8th term from the last is 30 and the last term is 65, is -5

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