A.P.: (2,6,10,14,\ldots)
(a=2), (d=4)
[ S_n=\dfrac{n}{2}[4+(n-1)4]=\dfrac{n}{2}\cdot4n=2n^2 ]
[ 2n^2>2000\implies n^2>1000\implies n\ge32 ] ((31^2=961), (32^2=1024))
Answer: 32 terms
11TH•Mathematics•Sequences And Series•Question 13
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The first four terms of an A.P. are 2, 6, 10 and 14. Find the least number of terms needed so that the sum of the terms is greater than 2000.
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