Arithmetic sequences

9000065309

Level:

The arithmetic sequence satisfies $a_{26} = 58$ and $a_{21} = 43$. Find the first term $a_{1}$ and the common difference $d$ of this sequence.

$a_{1} = -17;\ d = 3$

$a_{1} = -1;\ d = 5$

$a_{1} = 1;\ d = 15$

$a_{1} = -1;\ d = 3$

1003057906

Level:

The sum of the first $ 15 $ terms of an arithmetic sequence is $ 210 $ and the $ 15 $th term is $ 7 $. Choose the correct formula of calculation of the first term.

$ a_1=\frac2{15}\cdot210-7 $

$ a_1=\frac2{15}\cdot\frac{210}7 $

$ a_1=\frac{15}2\cdot210-7 $

$ a_1= \frac{210}7 $

$ a_1=\frac2{15} (210-7) $

1003057907

Level:

The sum of the first $ 25 $ terms of an arithmetic sequence is $ 700 $ and the first term is $ 4 $. Choose the incorrect statement about its common difference.

$ d $ is an odd number

$ d < 4 $

$ d > 0 $

$ d $ is a divisor of $ 48 $

1003057908

Level:

The $ 3 $rd term of an arithmetic sequence is $ 2 $ and the $ 20 $th term is $ 53 $. Find the sum of the first $ 13 $ terms.

$ 182 $

$ 358 $

$ 364 $

$ 689 $

$ 106 $

1003057909

Level:

The $ 2 $nd term of an arithmetic sequence is $ 100 $ and the common difference is $ -2 $. Choose the correct statement about the sum of the first $ 100 $ terms.

$ s_{100} > 200 $

$ s_{100} > 0 $ and $ s_{100} < 200 $

$ s_{100} < 0 $ and $ s_{100} > -100 $

$ s_{100} < -100 $

$ s_{100}=0 $

1003057910

Level:

The sum of the first $ n $ terms of an arithmetic sequence is $ 0 $, the common difference is $ 3 $ and the first term is $ -45 $. Find the $ n $.

$ 31 $

$ 15 $

$ 30 $

$ 16 $

$ 32 $

1003085201

Level:

Find the sum of all even numbers which are greater than $6$ and smaller than $122$.

$3648$

$3584$

$3654$

$3712$

$3776$

1003085202

Level:

What is the sum of all two-digit numbers divisible by five?

$945$

$950$

$1050$

$1045$

$940$

1003085203

Level:

What is the sum of all positive multiples of $7$ smaller than $100$?

$735$

$637$

$728$

$105$

$686$

1003085204

Level:

Evaluate the sum: $\sum\limits_{n=3}^{15}(-2n+5)$.

$-169$

$299$

$-156$

$-338$

$-312$

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