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Arithmetic Progressions
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01/06/2021 11:40 am
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In an AP
(i) Given a = 5, d = 3, an = 50, find n and Sn.
(ii) Given a = 7, a13 = 35, find d and S13.
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01/06/2021 11:42 am
(i) Given that, a = 5, d = 3, an = 50
an = a +(n −1)d,
⇒ 50 = 5+(n -1)×3
⇒ 3(n -1) = 45
⇒ n -1 = 15
⇒ n = 16
Now, sum of n terms,
Sn = n/2 (a +an)
Sn = 16/2 (5 + 50) = 440
(ii) Given that, a = 7, a13 = 35
an = a+(n−1)d,
⇒ 35 = 7+(13-1)d
⇒ 12d = 28
⇒ d = 28/12 = 2.33
Now, Sn = n/2 (a+an)
S13 = 13/2 (7+35) = 273