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An AP is given by k,2k/3,k/3,0 .....Find the sixth term. find the nth term. If the 20th term is equal to 15, find k​

User Rantanplan
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Answer:

  • 6th term: 8k/3
  • n-th term: an = k + (k/3)(n -1)
  • k = 45/22 for 20th term = 15

Explanation:

You know the general term of an AP is ...

an = a1 +d(n-1)

Here, a1 = k. The common difference is ...

2k/3 -k = -k/3

So, the general term is ...

an = k +(k/3)(n -1) . . . . the general term

__

The 6th term is then ...

a6 = k + (k/3)(6 -1) = (3k +5k)/3 = 8k/3 . . . . 6th term

__

The 20th term is ...

a20 = k + (k/3)(20 -1) = 22k/3

If this is 15, then the value of k is ...

22k/3 = 15

22k = 45

k = 45/22 . . . . value of k for a20 = 15

User JonathanKingston
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