Sum of the first 31 terms of an arithmetic sequence is 620
(a) what is its 16th term
(b) what is the sum of the 15th and 17th term
(c) Find the sum of first and 31st term
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The sum of the 1st and 17th terms of an arithmetic sequence is 40. The sum of its 1st and 18th terms is 43. What is the common difference?
The sum of the 1st and 17th terms of an AP = a +a+16d = 40, or
2a+16d = 40, or
a + 8d = 20 , or
a = 20–8d…(1)
The sum of the 1st and 18th terms of the AP = a +a+17d = 43, or
2a+17d = 43, or
2a = 43–17d …(2)
From (1) and (2)
40–16d = 43–17d, or
17d-16d = 43–40, or
d = 3.
From (1), a = 20 -3d = 20–3*8 = 20–24 = -4.
The common difference is 3.
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