the 16thterm of an AP is thrice the 5thterm . if the 12th term is 20 more than the 7th term . find the first term and the common difference
Answers
Answer:
16th term is 16
Step-by-step explanation:
Given : The fifth term of an A. P. is thrice the second term and 12th term exceeds twice the 6th term by 1.
To find : The 16th term.
Solution : The general form of an Arithmetic Progression is
a, a+d, a+2d, a+3d and so on.
Thus, nth term of an AP series is
where = nth term , a = first term , d= common difference
Now,
Situation 1 - The fifth term of an A. P. is thrice the second term
......[1]
Situation 2- 12th term exceeds twice the 6th term by 1.
.......[2]
From equation [1] put value of d in equation [2]
Now, put value of a in d we get,
Therefore, a=1 and d=2
So, 16th term
Hence, 16th term is 16.
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