Q4 of 50 Page 26

Write four arithmetic sequences with 100 as the sum of the first four terms.

Sn = 100 where n = 4


For an AP with a = first term


d = common difference


Sn =


∴ 2a + (4-1) × d = 50


∴ 2a + 3d = 50


Let a = 1, hence d = 16


Sequence is 1,17,33,49…


Let a = 4, hence d = 14


Sequence is 4,18,32,46…


Let a = 7 hence d = 12


Sequence is 7,19,31,43…


More from this chapter

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2

The first term of an arithmetic sequence is 1 and the sum of the first four terms is 100. Find the first four terms.

 3

Prove that for any four consecutive terms of an arithmetic sequence, the sum of the two terms on the two ends and the sum of the two terms in the middle are the same.

 5

The 8th term of an arithmetic sequence is 12 and its 12th term is 8. What is the algebraic expression for this sequence?

 6

The Bird problem in Class 8 (The lesson, Equations) can be slightly changed as follows.

One bird said:


“We and we again, together with half of us and half of that, and one more is a natural number”


Write the possible number of birds in order. For each of these, write the sum told by the bird also.


Find the algebraic expression for these two sequences.