Sample Questions on Progression

Q1: Find the nth term for the AP: 11, 17, 23, 29, …

Solution: 

Here, a = 11, d = 17 – 11 = 23 – 17 = 29 – 23 = 6We know that nth term of an AP is a + (n – 1) d=> nth term for the given AP = 11 + (n – 1) 6=> nth term for the given AP = 5 + 6 nWe can verify the answer by putting values of ‘n’.=> n = 1 -> First term = 5 + 6 = 11=> n = 2 -> Second term = 5 + 12 = 17=> n = 3 -> Third term = 5 + 18 = 23and so on … 

Q2: Find the sum of the AP in the above question till the first 10 terms.

Solution : 

From the above question, => nth term for the given AP = 5 + 6 n=> First term = 5 + 6 = 11=> Tenth term = 5 + 60 = 65=> Sum of 10 terms of the AP = 0.5 n (first term + last term) = 0.5 x 10 (11 + 65)=> Sum of 10 terms of the AP = 5 x 76 = 380 

Q3: For elements 4 and 6, verify that A ≥ G ≥ H.

Solution : 

A = Arithmetic Mean = (4 + 6) / 2 = 5G = Geometric Mean = = 4.8989H = Harmonic Mean = (2 x 4 x 6) / (4 + 6) = 48 / 10 = 4.8Therefore, A ≥ G ≥ H 

Q4: Find the sum of the series 32, 16, 8, 4, … upto infinity.

Solution : 

First term, a = 32Common ratio, r = 16 / 32 = 8 / 16 = 4 / 8 = 1 / 2 = 0.5We know that for an infinite GP, Sum of terms = a / (1 – r)=> Sum of terms of the GP = 32 / (1 – 0.5) = 32 / 0.5 = 64 

Q5: The sum of three numbers in a GP is 26 and their product is 216. ind the numbers.

Solution: 

Let the numbers be a/r, a, ar.=> (a / r) + a + a r = 26=> a (1 + r + r²) / r = 26Also, it is given that product = 216=> (a / r) x (a) x (a r) = 216=> a³ = 216=> a = 6=> 6 (1 + r + r²) / r = 26=> (1 + r + r²) / r = 26 / 6 = 13 / 3=> 3 + 3 r + 3 r² = 13 r=> 3 r² – 10 r + 3 = 0=> (r – 3) (r – (1 / 3) ) = 0=> r = 3 or r = 1 / 3Thus, the required numbers are 2, 6 and 18.

Progression (or Sequences and Series) are mathematical concepts that involve arranging numbers in a particular order based on a repeatable pattern. The topic of Progressions is frequently asked in various competitive exams like SSC, Bank PO, and other government job exams and is a crucial part of Quantitative Aptitude, but it can be mastered with the right formulas and working through some examples. 

Practice Quiz: 

Practice Progression Aptitude Quiz Questions