Arithmatic & Geometric Progression

Arithmatic Progression

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Arithmatic Progression

  • e.g. the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2.
  • The formula of nth term of sequence : an=a1+(n-1)d.where,
  • an : nth term of the sequence.
  • a1 : 1st term of the sequence.
  • n : Number of terms.
  • d : Difference between two consecutive terms.

  • Q.:-Write the first three terms in each of the following sequences defined by the following: (i) an = 7 n + 2 (ii) an = (28 n − 5)/(10) (iii) a1 = a2 = 28, an = an-1–7, n > 2



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  • Q. What is the 24th term of the sequence defined by , an = (n – 1) (2 – n) (3 + n) ?



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  • Q. First term is of arithmatic progression sequence is 20 and the difference between consecutive numbers is 10 , Find the numbers from 17 to 21 terms.



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  • Which n term of the AP : 4, 8, 12, . . . is 72 ?



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  • How many two-digit numbers are divisible by 6 ?



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  • If the sum of the first 11 terms of an AP is 253 and its first term is 3 , find the 20th term.



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  • Which term of the AP : 21, 18, 15, . . . is – 81? Also, is any term 0? Give reason for your answer.



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  • Q.:-Write the first three terms in each of the following sequences defined by the following: (i) an = 8 n + 6 (ii) an = (29 n − 3)/(8) (iii) a1 = a2 = 29, an = an-1–8, n > 2



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  • Q. What is the 49th term of the sequence defined by



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  • Q. First term is of arithmatic progression sequence is 45 and the difference between consecutive numbers is 6 , Find the numbers from 45 to 49 terms.



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  • Q. Insert 7 numbers between 4 and 34 such that the resulting sequence is an A.P.



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  • Array ( [0] => Q. There are n arithmetic mean(A.M'.) between 8 and 16 . The retio of the last mean to the first mean is 10:7 . find the value of n.



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  • Q. First term is of arithmatic progression sequence is 22 and the difference between consecutive numbers is 7 , Find the sum numbers from 54 terms.



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  • Q. First term is of arithmatic progression sequence is 46 and the difference between consecutive numbers is 12 , Find the sum numbers 5th, 6th, 7th, 8th and 9th terms.



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  • Q. First term is of arithmatic progression sequence is 54 and the difference between consecutive numbers is 7 , Find the sum numbers from 26 to 30 terms.



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Geometric Progression

  • Q. Find the 15th and nth terms of the G.P. 2,4,8,16, .....



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  • Q. First term is of geometric progression sequence is 50 and the common retio numbers is 6 , Find the numbers from 4 to 8 terms.



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  • Q.1. Find the 5th terms of the G.P. 2, 4, 8, 16, … .



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  • Q. In a G.P., the 5th term is 144 and the 9th term is 2304 . Find the first term(a), common ratio(r) and 14th term.



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  • Q.Insert 5 numbers between 9 and 576, so that the resulting sequence is a G.P.



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  • Q. First term is of geometric progression sequence is 5 and the common ratio numbers is 2 , Find the sum numbers from 5 to 9 terms, and sum of nth term.



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