PROGRESSION

PROGRESSION

1. What is an arithmetic progression?

   • An arithmetic progression is a sequence whose terms go up or down by constant steps. Ex: 3,6,9,12,15,18...
     • What are the formulas used for arithmetic progression?
       • To find the value of a certain term, use this formula: Tn = a + (n - 1) d, where a = 1st term, n = number of terms, d = common difference.
         • Example Questions:
       • To find the sum of all terms in a sequence, use this formula: Sn = n÷2 [ 2a + (n-1) d], where n= number of terms, a = first term and d = common difference.
         • Example Questions:
           • In this arithmetic progression, the first 3 terms and the last term are given. Find the number of terms. 3 9 15...525
           • Find the sum of the given number of terms of the following arithmetic series. 4 + 11 + 18 +... (15 terms)

2. What is a geometric progression?

   • A geometric progression is a sequence where each term after the first is multiplied by an integer which is also known as the common ratio. Ex: 2,8,32,128,512 has a common ratio of 4 as the numbers are consecutively multiplied by 4.
     • What are the formulas used for geometric progression?
       • To find the value of a certain term, use this formula. Tn = ar^n-1, where a = first term, r = common ratio and n = number of terms
       • To find the sum of all terms in a sequence, use this formula.
         • • Example Questions
             • Find the 6th term of the geometric progression: 2,10,50,...
             • Find the sum of the terms of the geometric progression: 24,12,6,3
             • Find the sum of infinity of the geometric progression: 5,10,20...
       • To find the sum of infinity, use this formula.
         • • Example Questions

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