Finite arithmetic series Quiz 1

Question 1

The first terms of two A.P. series are in the ratio $$9:10$$ respectively and the sum of their common differences is 7. The sum of the sum of the first fifteen terms of both the series is 2160 and the eleventh term of the second series is 200. What is the eleventh term of the first series?

Accepted Answer

-35

Answer

-42

Answer

35

Answer

30

Question 2

An arithmetic series consists of $$2n$$ terms, and the first term equals the value of the common difference. If a new series is formed taking the $$1st,3rd,5th,....\left( 2n-1 \right)th$$ term of the old series, find the ratio of the sum of the new series to that of the sum of the terms of the old series.

Accepted Answer

$$\dfrac{n}{2n+1}$$

Answer

$$\dfrac{2n}{2n-1}$$

Answer

$$\dfrac{2n}{2n+1}$$

Answer

$$\dfrac{n}{2n-1}$$

Question 3

The combined value of $${{a}_{8}}$$ and $${{a}_{18}}$$ of an arithmetic progression is equal to the combined value of $${{a}_{9}}$$, $${{a}_{11}}$$ and $${{a}_{14}}$$ of the same progression. Then which element of the series should necessarily be equal to zero?

Accepted Answer

8th

Answer

6th

Answer

1st

Answer

10th

Question 4

If in the given series the difference between the consecutive terms forms an arithmetic progression and also the 1st, 4th and 7th term of that given series is 3, 18 and 51 respectively, then find the sum of the first 6 terms of this series?

Accepted Answer

103

Answer

100

Answer

92

Answer

88

Question 5

An arithmetic progression is given; $$3,6,9,12,....$$ Find the sum of the squares of the first 20 terms.

Accepted Answer

25830

Answer

23102

Answer

28500

Answer

31092