Question

Find the 8th term of ap is 95,91,87,83

Answer 1

1st Method:
8th term = a+7d = 39 ........... (i)
12th term = a+11d = 59 ........... (ii)
(i)-(ii);

Or, a+7d-a-11d = 39-59; Or, 4d = 20;
Or, d = 5;
Hence, a+7*5 = 39;
Thus, a = 39-35 = 4.
2nd Method (Thought Process): 
8th term = 39;
And, 12th term = 59;
Here, we see that 20 is added to 8th term 39 to get 12th term 59 i.e. 4 times the common difference is added to 39.
So, CD = 20/4 = 5.
Hence, 7 times CD is added to 1st term to get 39. That means 4 is the 1st term of the AP.

Answer 2

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GIVEN :

The AP is 95,91,87,83,....

TO FIND :

The 8th term of an AP

ANSWER :

From the given AP,

The first term , a = 95

The common difference, d = t2 - t1

d = 91 - 95

d = - 4

The general term,tn =

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

where n is the nth term.

a is the first term.

d is the common difference.

t8 = a + ( 8 - 1) d

= 95 + 7d

= 95 + 7 (-4)

= 95 - 28

= 67

t8 = 67

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