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प्रश्न
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.)
उत्तर
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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