An arithmetic progression or arithmetic sequence (AP) is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression. Here are some math progressions: Arithmetic progression: Also known as an arithmetic sequence, this is a mathematical progression where the difference between two consecutive terms is the same. The constant is known as the common difference. Geometric progression: In this mathematical sequence, each succeeding term is... Show more

An arithmetic progression or arithmetic sequence (AP) is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.

Here are some math progressions:
Arithmetic progression: Also known as an arithmetic sequence, this is a mathematical progression where the difference between two consecutive terms is the same. The constant is known as the common difference.
Geometric progression: In this mathematical sequence, each succeeding term is formed by multiplying the preceding term by a specific fixed number.
Harmonic progression: This is a mathematical progression created by taking the reciprocals of an arithmetic progression.
Proportionality: This progression describes how the study of ratios and proportional relationships extends students' work in measurement and in multiplication and division in the elementary grades.
Navigation: This mathematical subject requires knowledge of arithmetic, geometry, algebra, analytical geometry, and plane trigonometry.
 

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Math Practice Test: Progression

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14 Questions

1. The length of a side of a square is a meters. A second square is found by joining middle points of this square is formed by joining the middle points of the second square and so on, the process is carried on Find the sum of the areas of all such infinite squares.

4a2a22a2

2. Find the sum of integers from 1 to 100 which are divisible by 2 and/or 5.

3050105025503200

3. A G. P. consists of an even number of terms. The sum of all the terms is three times that of the odd terms. Determine the common ratio of the GP

231/21

4. The first and the last term of an AP are a and L respectively. If S is the sum of all the terms of the AP then the common difference expressed in terms of a, L and S is_____

(L − a)/S(L2 − a2)/2S(L2 − a2)/[2S − (L + a)](L − a)/(S1)

5. Sum the series (a + b) + (a2 + 2b) + (a2 + 3b) + ..... to a terms.

a(a2−1)/(a−1)+b n(n+1)/2ab, n(n+1)/2a(a2−1)/(a−1)+b2(b+1)/2a(a21)/(a1)+b(b+1)/2

6. 150 workers were engaged to finish a piece of work in a certain number of days. 4 workers dropped on the second day, 4 more dropped the third day and so on. It took 8 more days to finish the work now. Find the number of days in which the work was scheduled to be completed?

24253233

7. 21/4 + 21/16 + 21/32_____ =

21/21/

8. Certain numbers appear in both arithmetic progressions 17, 21, 25,..… and 16, 21, 26….. find the sum of first five numbers appearing in both progressions.

101305426204

9. The third term of a G. P. is 4, then the product of the first five terms is:

43none of these4544

10. Find the sum of first and the last terms of an AP a1, a2, a3.....if we know that a1 + a10 + a15 + a20 + a24 = 225

150cannot be determined.75225

11. Along a road lie odd number of stones placed at a distance of 10 m. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man carried the job with one of the end stones by carrying them in succession. In carrying all the stones he covered a distance of 3 km. Find the number of stones.

20151025

12. If (51 + x + 51 - x) + (25x + 25−x) = a, then for what value of “a” will x have a solution?

a ≤ 2a ≤ 4a ≤ 6a ≤ 12

13. If S1, S2, S3,... Sn are the sum of infinite geometric series whose first terms are 1, 2, 3,…n and whose common ratios are 1/2, 1/3, 1/4….1(n+1) respectively, then find the value of S1, S2, S3,...Sn

n(n+3)/2n2+1n +1n (n+1)/6

14. Find the sum of 2 n terms of a series of which every even term is a times the item before it, and every odd term c times the term before it, the first term being unity.

(an 1)/(a1)+(cn1)/(c1)(an1)/(a1)+ c(cn1)/(c1)(a+1) (1ancn)/(1Ac)(1+ac)(1ancn)/(1ac)