Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.
Select the correct option.
A) 5	B) 6	C) 4	D) 3	E) 7
Solution: 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= 
<gadget id="calculator">39-35</gadget>
<output>4</output>
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= 
<gadget id="calculator">20/4</gadget>
<output>5</output>
5.   Hence, 7 times CD is added to 1st term to get 39. That means 4 is the 1st term of the AP.   Answer: Option 4
<result>C</result>
Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.