Arithmetic sequences

Sum of Terms of Arithmetic Sequences I

Submitted by ladislav.foltyn on Sat, 02/23/2019 - 13:57

1003097008

Level:

Find the first term of an arithmetic sequence

{a_{n}}_{n = 1}^{\infty}

, if the sum of the first eight terms is

12

and the sum of the first twelve terms is

- 6

\begin{aligned} s_{8} & = 12 \\ s_{12} & = - 6 \end{aligned}

5

- 5

2

1

- 3

1003097007

Level:

Find the common difference of an arithmetic sequence

{a_{n}}_{n = 1}^{\infty}

, if the sum of the first seven terms is

42

and

a_{10} = - 4 a_{5}

\begin{aligned} s_{7} & = 42 \\ a_{10} & = - 4 a_{5} \end{aligned}

- 3

3

15

2

- 2

1003097006

Level:

Find the sum of the first ten terms of an arithmetic sequence

{a_{n}}_{n = 1}^{\infty}

, if:

\begin{aligned} a_{1} + a_{5} + a_{10} & = 40 \\ a_{10} - a_{5} - a_{1} & = 24 \end{aligned}

140

180

160

320

200

1003097005

Level:

Find the square of the first term of an arithmetic sequence

{a_{n}}_{n = 1}^{\infty}

, if:

\begin{aligned} a_{2}^{2} + a_{3}^{2} & = 100 \\ a_{5} + a_{7} & = 0 \end{aligned}

100

196

64

169

200

1003097004

Level:

Find the third term of an arithmetic sequence

{a_{n}}_{n = 1}^{\infty}

, if:

\begin{aligned} 2 a_{10} - 3 a_{3} & = 5 \\ 5 a_{5} + 4 a_{1} & = 83 \end{aligned}

9

7

1

3

11

1003097003

Level:

Find the sum of the first five terms of an arithmetic sequence

{a_{n}}_{n = 1}^{\infty}

, if:

\begin{aligned} a_{1} \cdot a_{4} & = 100 \\ a_{2} + a_{6} & = 10 \end{aligned}

50

0

20

- 5

90

1003097002

Level:

Find the common difference of an arithmetic sequence

{a_{n}}_{n = 1}^{\infty}

, if:

\begin{aligned} a_{11} + a_{4} & = - 19 \\ a_{6} + a_{7} & = - 13 \end{aligned}

- 3

3

7

- 1

10

1003097001

Level:

Find the first term of an arithmetic sequence

{a_{n}}_{n = 1}^{\infty}

, if:

\begin{aligned} a_{2} + a_{9} & = 24 \\ a_{8} - a_{6} & = 4 \end{aligned}

3

6

2

10

1

1003085104

Level:

The

n

th term of an arithmetic sequence is

1 - 3 n

. Find the

5

th term and the common difference.

a_{5} = - 14; d = - 3

a_{5} = - 2; d = - 3

a_{5} = 14; d = - 3

a_{5} = - 14; d = 3

a_{5} = - 2; d = 3

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Sum of Terms of Arithmetic Sequences I

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