Mathematics
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.).
AP
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Answer
The given A.P. is 15, 30, 45, 60,……
a = 15
d = 30 - 15 = 15
an = 300
We know that,
∴ an = a + (n - 1)d
⇒ 300 = 15 + (n - 1)15
⇒ 300 - 15 = (n - 1) 15
⇒ 285 = (n - 1)15
⇒ = n - 1
⇒ 19 = n - 1
⇒ n = 19 + 1
⇒ n = 20
We know that,
Sum of n terms of an A.P. is given by,
∴ Sn = (a + l)
Now we have,
a = 15
n = 20
l = 300
⇒ S20 = (15 + 300)
= 10 (315)
= 3150
Hence, S20 = 3150.
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