Practice Questions for Algebra - Progressions

1. PE 4 - Progression | Algebra - Progressions

A student in a class wrote down the first n natural numbers and calculated their sum. While calculating the sum, he forgot to add two consecutive numebers and got the sum as 7,370. Find the two numbers that she forgot to add.

(a)
4 and 5
(b)
5 and 6
(c)
6 and 7
(d)
7 and 8
(e)
Cannot be determined

2. PE 4 - Progression | Algebra - Progressions

Find the ratio of 4^th and 13^th term of the series: $\frac{1}{4}$ + $\frac{3}{16}$ + $\frac{3}{20}$ + ...

(a)
5 : 2
(b)
4 : 13
(c)
5 : 3
(d)
7 : 2

3. PE 4 - Progression | Algebra - Progressions

In how many ways can 111 be written as the sum of three distinct integers in geometric progression?

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7 8 9 4 5 6 1 2 3 0 . -

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4. PE 4 - Progression | Algebra - Progressions

Find the sum of first 10 terms of the series 2 + 22 + 222 + ....

(a)
$\frac{2}{9}$ × $[\frac{10^{11} - 100}{9}]$
(b)
$\frac{2}{9}$ × $[\frac{10^{11} - 90}{9}]$
(c)
$\frac{2}{9}$ × $[\frac{10^{11} + 90}{9}]$
(d)
$\frac{2}{9}$ × $[\frac{10^{10} - 100}{9}]$
(e)
None of these

5. PE 4 - Progression | Algebra - Progressions

Find the sum of the first 20 terms of the sequence 2, 3, 5, 7, 8, 11, …

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7 8 9 4 5 6 1 2 3 0 . -

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6. PE 4 - Progression | Algebra - Progressions

If the ratio of 5^th terms of two Arithmetic Progressions is same as the ratio of their 9^th terms, what is the ratio of their common differences?

(a)
2 : 3
(b)
1 : 2
(c)
2 : 1
(d)
1 : 1
(e)
Cannot be determined

7. PE 4 - Progression | Algebra - Progressions

The first, second and last terms of an A.P. respectively are x, y and 2x. Find the sum of all the terms in the A.P.

(a)
$\frac{xy}{(y - x)}$
(b)
$\frac{2 xy}{3 (y - x)}$
(c)
$\frac{3 xy}{2 (y - x)}$
(d)
$\frac{3 xy}{4 (y - x)}$

8. PE 4 - Progression | Algebra - Progressions

In an A.P., the sum of first a terms is X & sum of first 2a terms is Y. If X = 3Y/4, find the sum of the first 3a terms of the A.P.

(a)
X + Y
(b)
Y - X
(c)
X
(d)
Y
(e)
None of these

9. PE 4 - Progression | Algebra - Progressions

Find the sum of 1² - 2² + 3² - 4² + ... + 49² - 50².

(a)
-1275
(b)
-1250
(c)
1275
(d)
1325
(e)
None of these

10. PE 4 - Progression | Algebra - Progressions

Consider 5 numbers p, q, r, s & t such that p, q and r are in A.P., q, r and s are in G.P. and r, s and t are in H.P. p, r and t will form a/an

(a)
AP
(b)
GP
(c)
HP
(d)
AP or GP

PE 4 - Progression | Algebra - Progressions

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