An arithmetic progression has 2nd term = 20 and 8th term = 60. What is the 20th term?
- 100
- 140
- 180
- 200
Explanation
aₙ = a + (n - 1)d
Let a be the first term, d the common difference.
Given:
2nd term: a + d = 20
8th term: a + 7d = 60
Subtract the two equations:
(a + 7d) - (a + d) = 60 - 20
6d = 40 ⇒ d = 40 / 6 = 20 / 3
Now plug d = 20/3 into a + d = 20:
a = 20 - 20/3 = (60 - 20)/3 = 40/3
Now find the 20th term:
a + 19d = 40/3 + 19 × (20/3) = (40 + 380)/3 = 420/3 = 140
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