Dear students, you know that QUANT is a part of getting points and every chapter is important. Therefore, we are providing notes on basic concepts of Arithmetic And Geometric Progression with formulas and some questions which you can practice after reading out concepts and formula. Read all these formulas and solve all the question and practice well for your upcoming exams. These notes and questions are based on latest pattern of RRB ALP/Group D exam.
Arithmetic Progression :
Series of the form a, a + d, a + 2d, a + 3d . . . . . . . . . . is called Arithmetic Progression, when they increase or decrease by a common difference
e.g.→ 5, 12, 19, 26, 33
Common difference, d = 12 – 5 = 7
19 – 12 = 7
26 – 19 = 7
a₁, a₂, a₃ . . . . . . . . . . ,Tn
d = common difference = 2nd term – Ist term = a₂ – a₁
Last Term = a+(n-1)d
a → 1st term
n → no. of terms
d → Common difference
Sum of n terms in A.P :
Sum of n terms = n/2 [2a+(n-1)d]
Or
Sum of n terms = n/2 [First term+last term]
Total no. of term = (Last term-First term)/(Common difference )+1
Q1. 1, 4, 6, 5, 11, 6 . . . . . . Find the sum first 100 terms?
1, 4, 6, 5, 11, 6 . . . . . . पहले 100 पदों का योग ज्ञात कीजिए?
(a) 7600
(b) 7800
(c) 7900
(d) 8000
Q2. Find the sum of all 2 digits no. which will exactly divided by 9?
सभी 2 अंकों की संख्या का योग ज्ञात कीजिए जो ठीक 9 से विभाज्य होंगे?
(a) 565
(b) 585
(c) 525
(d) 575
Q3. If T₂ + T₅ = 8 of an A.P & T₃ + T₇ = 14 of that A.P then, find the 11th term?
यदि एक अंकगणितीय प्रगति का T₂ + T₅ = 8 होता है और उस अंकगणितीय प्रगति का T₃ + T₇ = 14 होता है तो उसका 11वां पद ज्ञात कीजिए?
(a) 20
(b) 21
(c) 22
(d) 19
Q4. If t₁ + t₅ + t₁₀ + t₂₀ + t₂₄ = 225 , Find the sum of first 23rd term of that A.P?
यदि t₁ + t₅ + t₁₀ + t₂₀ + t₂₄ = 225 तो उस अंकगणितीय प्रगति के पहले 24 वें पदों का योग ज्ञात कीजिए?
(a) 800
(b) 700
(c) 850
(d) 1035
Geometric Progression :
a, ar, ar², ar³ . . . . . . . . . . . . . .
Common Ratio (r) = (Second term)/(First term)
Last term of GP =
Sum of n terms in G.P =
, where r > 1
, where r > 1
Or
Sum Of n terms in G.P =
, where r<1
, where r<1
Sum of an Infinite Geometric Progression, when r < 1
Q1. The 7th term of G.P is 8 times the 4th term. What will be the 1st term if its 5th term is 48?
ज्यामितीय प्रगति का सातवाँ पद चौथे पद का 8 गुना है. पहला पद क्या होगा यदि उसका पांचवां पद 48 है?
(a) 5
(b) 6
(c) 3
(d) 7
Some other Important Formulas :
Q1. The sum of first 29 odd natural number is equal to?
पहली 29 विषम संख्याओं का योग बराबर है:
(a) 1000
(b) 625
(c) 729
(d) 841
Q2. The Sum of first 100 even natural numbers is equal to?
पहली 100 सम संख्याओं का योग बराबर है:
(a) 10100
(b) 10200
(c) 10300
(d) 10400
Q3. The sum of squares of first 50 natural numbers is equal to?
पहली 50 प्राक्रतिक संख्याओं के वर्गों का योग बराबर है:
(a) 42925
(b) 43935
(c) 44945
(d) 45955
Q4. The sum of first 500 natural numbers is equal to?
पहली 500 प्राक्रतिक संख्याओं का योग बराबर है:
(a) 125250
(b) 124240
(c) 126260
(d) 127270
Q5. The sum of cubes of first 30 numbers is equal to?
पहली 500 प्राक्रतिक संख्याओं का योग बराबर है:
(a) 210225
(b) 216225
(c) 400225
(d) 420225
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