QQuestion
Which term of the Arithmetic Progression 15, 30, 45, 60, … is 300? Hence, find the sum of all the terms of the A.P. up to 300.
✓Answer
Given A.P.: 15, 30, 45, 60, …
First term, a = 15
Common difference, d = 30 − 15 = 15
Let the nth term be 300.
⇒ aₙ = a + (n − 1)d
⇒ 300 = 15 + (n − 1)15
⇒ 300 = 15 + 15n − 15
⇒ 300 = 15n
⇒ n = \frac{300}{15}
⇒ n = 20
Therefore, 300 is the 20th term.
Now,
⇒ Sₙ = \frac{n}{2}(a + aₙ)
⇒ S₂₀ = \frac{20}{2}(15 + 300)
⇒ S₂₀ = 10 × 315
⇒ S₂₀ = 3150
Therefore, the sum of all terms up to 300 is 3150.
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