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Arithmetic Sequences - Questions

Question 1
24641

The fifth term of an arithmetic sequence is 44, and the tenth term is 64

(i) Find the value of the first term and the common difference.

(ii)  Find the sum of the first 100 terms.

(i)  The first term is 28 and the common difference is 4.

(ii) \({S_{100}} = 22,600\)

Question 2
24642

For the multiples of 6 between 100 and 200, find

(i)  the last multiple

(ii)  the first multiple

(iii)  the number of multiples between 100 and 200

(iv)  the sum of the multiples between 100 and 200

(i)  198

(ii)  102

(iii)  \(n = 17\)

(iv)  \({S_{17}} = 2550\)

Question 3
24643

Find the 10th term of the arithmetic series \(\sqrt 3 + \sqrt 2 ,\,2\sqrt 3 ,\,3\sqrt 3 - \sqrt 2 ,...\)

\(10\sqrt 3 - 8\sqrt 2 \)

Question 4
24644

The sum of the first \(n\) terms of an arithmetic series is \({S_n}\) where \({S_n} = {n^2} - 2n\), find

(i)  the \(n\)th term

(ii)  the fourth term

(i)  \({T_n} = 2n - 3\)

(ii)  \({T_4} = 5\)

Question 5
11983

Find the 21st term in the arithmetic sequence 1,4,7,....

61

Question 6
11984

Find the number of terms in the arithmetic sequence 67,60,53,...., -143

31

Question 7
12000

Find the \({19}^{th}\) term of the arithmetic sequence 3, 11, 19, ...

\({T_{19}} = 147\)

Question 8
12001

Find the \({42}^{nd}\) term of the arithmetic sequence \(7,\,6\frac{1}{2},6\), ...

\({T_{42}} = - 13.5\)

Question 9
12002

Find the number of terms in the arithmetic sequence 2, 4, 6, ..., 46

23

Question 10
12003

Find the number of terms in the arithmetic sequence 407, 401, ..., -133

91

Question 11
12004

The 2nd term of an AP is 15 and the 5th term is 21. The first term \(a\) and the common difference \(d\) are?

\(a = 13, d = 2\)

Question 12
124527

A series is given by \(\log _{10} e+\log _{10} e^2+\log _{10} e^3+\cdots+\log _{10} e^n\)

Show that this is an arithmetic series.

True

Question 13
51956

Find the first term of an arithmetic progression \(8,\,17,\,26,\,...\) that exceeds \(500\)

\(503\)