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
E. 7
Answer: Option C
Solution(By Examveda Team)
1st Method: 8th term = a + 7d = 39 ........... (i) 12th term = a + 11d = 59 ........... (ii) (i) - (ii); Or, a + 7d - a - 11d = 39 - 59Or, 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 = $$\frac{{20}}{4}$$ = 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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Related Questions on Progressions
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
E. 7
The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is
A. 600
B. 765
C. 640
D. 680
E. 690
See 2nd term a +d, so 4+5=9,common difference=9_5=4ans