Sequences & Series

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IB: Max

Perplexing

IB: 4

1

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0 / 6

An arithmetic sequence has 2u6=S6=5, where S6 is the sum of the first 6 terms. Find the second term, u2, of the sequence.

[6]

2

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0 / 6

An arithmetic sequence has u3=5 and u7=−7.

Find the common difference d and the first term u1 of the sequence.
[3]
Hence find u10.
[1]
Find S10.
[2]

3

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0 / 5

A geometric sequence has u3=3 and u6=98. Find S∞ for this sequence.

[5]

4

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0 / 6

Ella invests $500 in a savings account that earns 4% interest per annum, compounded quarterly.

Find an expression for the balance of Ella's savings after n years.
[2]
Calculate the value of Ella's savings after 12 years. Give your answer to the nearest dollar.
[2]

Ella wants to purchase a racing bike for $700.

Find the number of years after which her savings will be sufficient to purchase the bike.
[2]

5

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IB: 5

6

!

0 / 5

An arithmetic sequence has u9=20 and S12=180. Find the value of u1 and the value of d.

[5]

7

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0 / 5

Given that n=1∑15(5+kn)=−105, find the value of k.

[5]

8

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0 / 5

A stork delivers babies to families living on Dorchester avenue. The bird carries one baby at a time from its nest to each home on the street.

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The distance between the nest and the first house is x meters, and the distances between adjacent houses is 20 meters.

When delivering a baby to the 7th house on the street, the stork flies a round trip distance of 290 meters.

Determine the value of x.
[3]
Find the total distance, in kilometers, that the stork must fly to deliver 32 babies.
[2]

9

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