The sum of the first five terms of an arithmetic sequence is 150 and the sum of the first ten terms is 550
(a) what is the third term of the sequemce
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- sum of first five terms of AP = 150
- sum of first ten terms of AP = 550
- 3rd term.
Sum of first ten terms = 550
Solving (i) and (ii) by elimination method.
2a +4d = 60
2a +9d = 110
--⠀⠀ -- ⠀⠀--
⠀⠀⠀-5d = -50
d = 50/5
d = 10
putting value of d in (i)
⠀⠀⠀⠀⠀➝ 2a +4×10 = 60
⠀⠀⠀⠀⠀➝ 2a +40 = 60
⠀⠀⠀⠀⠀➝ 2a = 20
⠀⠀⠀⠀⠀➝ a = 20/2
⠀⠀⠀⠀⠀➝ a = 10
So, third term of AP = a +2d
⠀⠀⠀⠀⠀➝ 10 + 2 ×10
⠀⠀⠀⠀⠀➝ 10 + 20
⠀⠀⠀⠀⠀➝ 30
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