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Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.

A. 5 B. 6 C. 4 D. 3 Answer: Option C
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Solution(By Apex Team)

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 = $\Large\frac{20}{4}$ = 5 Hence, 7 times CD is added to 1st term to get 39. That means 4 is the 1st term of the AP

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