2002 A lvl Maths P1 Q10
Question from http://www.sgforums.com/forums/2297/topics/348847
An AP in which the common difference is twice the 1st term is called a special AP. Show that the sum of the first n terms of a special AP with 1st term a is n²a.
The (M-2)th term of a special AP is 663 and the Mth term is 731. Find M and find also the sum of the first M terms.
The sum of the first N terms of another special AP is S. Find in the terms of S, the sum of the next N terms.
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Answer:
Let first term = a, common difference = 2a
Sn = (n/2)*(2a + (n-1)(2a))
= (n/2)*(2a + 2an - 2a)
= (n/2)*(2an)
= n²a (shown)
Mth term - (M-2)th term = 2 * common difference
731 - 663 = 2 * 2a
a = 17, d = 34
731 = 17 + (M-1)(34)
M = 22
Sum of first M terms =22² * 17 = 8228
Sn = n²a
S2n = 4n²a
Difference of next N terms = S2n - Sn
= 3n²a
= 3S
