Chapter 4
Separation for Expiration of Service Obligation
4-1. Policy
A Soldier will be separated upon expiration of enlistment or fulfillment of service obligation.
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Chapter 4 on DD-214
I'll try to answer the question, "If the 5th term of a geometric progression is 2, then the product of its FIRST 9 terms is --?" Given the first term is A and the ratio is r, then the progression starts out... A, Ar, Ar^2, Ar^3, Ar^4, ... So the 5th term is Ar^4, which equals 2. The series continues... Ar^5, Ar^6, Ar^7, Ar^8, ... Ar^8 is the 9th term. The product P of all 9 terms is therefore: P = A * Ar * Ar^2 *...*Ar^8 Collect all the A's P = (A^9)*(1 * r * r^2 ...* r^8) P = A^9 * r^(0+1+2+...+8) There's a formula for the sum of the first n integers (n/2)(n+1), or if you don't know just add it up. 1+2+...+8 = 36 Therefore P = A^9 * r^36 Since 36 is a multiple of 9, you can simplify: P = (Ar^4)^9 Still with me? Remember that Ar^4=2 (a given fact). So finally P = 2^9 = 512. Cute problem.
there ar about 200- 100 -_200
This is a geometric sequence of the form a, ar, ar^2, ar^3, ... where a is the first term and r is the common ratio.In our case, the first term a = 2, and the common ratio r = 5.The nth term of such a sequence isan = a r^(n -1).
an = an-1 + d term ar-1 = 11 difference d = -11 ar = ar-1 + d = 11 - 11 = 0 The term 0 follows the term 11.