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Mathematics Grade 12 Unit 1: SEQUENCES AND SERIES

national exam questions have come from this unit. It runs 59 pages; one careful study pass takes about 6.1 hours, and its difficulty is harder among Mathematics units. Each section below lists the questions set from it, with the year, and opens the page that teaches it.

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1.1 Sequence · read p. 2

Not asked in a national paper yet.

1.2 Arithmetic and Geometric Sequences · read p. 9

2018 E.C., Q48 – In a geometric sequence, the first term is and the fifth term is (assume the common ratio is positive). What is the value of the 13th term ( )?
2018 E.C., Q47 – In an arithmetic progression, the first term is 11 and the common difference is –13. What is the sum of the first 7 terms?
2017 E.C., Q34 – Which of the following statement defines geometric progression?
2016 E.C., Q27 – For the arithmetic sequence with $A_3=5$ and $A_5=10$, which of the following is the sum of the first 20 terms?
2016 E.C., Q10 – If the fifth and the tenth terms of a geometric sequence are 640 and 20 respectively, then which of the following numbers are the first term and the common ratio of the given geometric sequence respectively?
2016 E.C., Q26 – Few terms of a sequence are given as follows: -2, 0, 4, 10, ... Which of the following can be a fifth term?
2014 E.C., Q38 – What is the seventh term of an arithmetic sequence whose third term is -4 and common difference is 3?
2013 E.C., Q27 – Which of the following is a geometric sequence?
2013 E.C., Q27 – Which of the following is a geometric sequence?

1.3 The Sigma Notation and Partial Sums · read p. 21

2017 E.C., Q41 – Which one of the following is equal to ?
2015 E.C., Q40 – If the 6 th and the 11 th term of an arithmetic sequence are 35 and 75 respectively, then what is the sum of the first 31 terms of the sequence?
2014 E.C., Q33 – The sum of the first 8 terms of a geometric sequence with first term $0.3$ and common ratio $1/10$ is equal to:
2013 E.C., Q26 – Which one of the following is the fourth term of the sequence $\left\{\ \cos(\frac{n\pi}{2}) \right\}$?

1.4 Infinite Series · read p. 35

2017 E.C., Q5 – When converting the recurring decimal into a fraction using convergent geometric series, then what are the first term and the common ratio respectively?
2016 E.C., Q27 – Which one of the following is equal to the sum $ \sum_{k=1}^{7} 729(3^{1-k}) $?
2016 E.C., Q28 – Suppose a and b are real numbers such that $a\ne 0$ and $b>0$. If $\sum_{n=1}^{\infty} b\left(\frac{a}{b}\right)^n$ converge, which of the following is true?
2015 E.C., Q33 – Let the sequence {a n } converges to 3 while {b n } converges to -1. Then the sequence {a n -b n } converges to
2015 E.C., Q2 – The solution set of the inequality $(2x - 3)(x + 5) \leq 0$ is
2015 E.C., Q25 – Which one of the following geometric series is convergent?
2013 E.C., Q29 – What is the least upper bound of the sequence $\left\{2 + \frac{n}{n+1}\right\}_{n=1}^\infty$?
2013 E.C., Q61 – Which of the following series is convergent?
2013 E.C., Q31 – Suppose ${a_n}$ and ${b_n}$ are sequences with $lim a_n = L and lim b_n = M$. Then which of the following is NOT necessarily true?
2013 E.C., Q32 – Suppose ${a_n}$ and ${b_n}$ are sequences with $\lim_{n\to\infty} a_n = L$ and $\lim_{n\to\infty} b_n = M$. Then which of the following is NOT necessarily true?

1.5 Applications of Sequence and Series in Daily life · read p. 44

2017 E.C., Q46 – Which of the following statement is true about the given infinite series?
2017 E.C., Q9 – Dibabe was hired in an elementary school with a monthly salary of Birr 30,000. The agreement was to raise her salary every year by Birr 3,000. What is the total amount of money that Dibabe will earn at the end of the 8th