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Question
Which term of the Arithmetic Progression (A.P.) 15, 30, 45, 60...... is 300?
Hence find the sum of all the terms of the Arithmetic Progression (A.P.)
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Solution
Given A.P. is 15, 30, 45, 60.........
Here a = 15, d = 30 – 15 = 15
Let Tn = 300
Tn = a + (n – 1)d
300 = 15 + (n – 1) × 15
300 = 15 + 15n – 15
15n = 300
∴ n = 20
Hence, 300 is the 20th term
Also by Sn = `n/2 [2a + (n - 1)d]`
S20 = `20/2 [2 xx 15 + (20 - 1) xx 15]`
= 10[30 + 285]
= 10 × 315
∴ S20 = 3150
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