in an Ap the 9th term is 73 and the 4th term is 43 what is the sum of the first 20 terms
Answers
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Given info : In an AP, 9th term is 73 and the 4th term is 43.
To find : The sum of the first 20 terms is ..
solution : we know, nth term of an AP is given as Tn = a + (n - 1)d , where a is first term and d is common difference.
9th term = 73 [ Given ]
⇒a + (9 - 1)d = 73
⇒a + 8d = 73 ....(1)
4th term = 43 [ Given ]
⇒a + (4 - 1)d = 43
⇒a + 3d = 43 ....(2)
subtracting eq (2) from eq (1) we get,
a + 8d - (a + 3d) = 73 - 43 = 30
⇒5d = 30
⇒d = 6
a = 43 - 3d = 43 - 3 × 6 = 43 - 18 = 25
now sum of first n terms is given as Sn = n/2 [2a + (n - 1)d]
here n = 20 , a = 25 , d = 6
so, S₂₀ = 20/2 [ 2 × 25 + (20 - 1) × 6 ]
= 10 [50 + 19 × 6 ]
= 10 [ 50 + 114 ]
= 10 × 164
= 1640
Therefore the sum of first 20 terms is 1640.
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