Q1 of 50 Page 26

Write three arithmetic sequences with 30 as the sum of the first five terms.

Sn = 30 where n = 5


For an AP with a = first term


d = common difference


Sn =


Substituting in above equation…


∴ 2a + (5-1) × d = 12


∴ 2a + 4d = 12


∴ a + 2d = 6


i) Let a = 2, hence d = 2


Sequence is 2,4,6,8,10…


ii) Let a = 4, hence d = 1


Sequence is 4,5,6,7,8…


iii) Let a = 6, hence d = 0


Sequence is 6,6,6,6,6…


Hence, 3 sequences are found.


More from this chapter

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6

Fill up the empty cells of the square below such that the numbers in each row and column from arithmetic sequences:

What if we use other numbers instead of 1, 4 28 and 7?


 7

In the table below, some arithmetic sequences are given with two numbers against each. Check whether each belongs to the sequence or not.

 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.