...But 2 X 2 = 2 2 , 2 X 2 X 2 = 2 3 , and 2 X 2 X 2 X 2 = 2 4 . Therefore, any term of the'progression is equal to the first term multiplied by the ratio raised to a power 1 less than the number of the term. CASE I. Having given the first term, the common ratio, and the...

...1 less than the number of terms : thus, 3=^3 1st term, 3x2 = 0 2d term, ' Therefore, the last term is equal to the first term multiplied by the ratio raised to a power 1 less than the number of terms. RULE. — Raise the ratio to a power whose exponent is 1 less than...

...following are the most useful principles relating to Geometrical Progression. Tlic Last Term. $ 34S. The last term of a geometrical progression is equal to the first term multiplied into that power of the ratio which is expressed by the number of terms less one. If the first term...

...following are the most useful principles relating to Geometrical Progression. The Last Term. § 349. The last term of a geometrical progression is equal to the first term multiplied into that power of the ratio which is expressed by the number of terms less one. If the first term...

...term is equal to the f1rst multiplied by the second power of the ratio ; that, in general, any term is equal to the first term multiplied by the ratio raised to a power whose exponent is less bv 1 than the number of that term. Hence, to find the last term, multiply the first term by the...

...c== bq = aq>, d = cq = aq3 from which it will be readily inferred, that a term of any rank whatever is equal to the first term multiplied by the ratio raised to a power, the exponent of which is one less than the number, which marks the place of this term. Let L designate...

...be If, therefore, we put I for the last term, and n the number of terms of the series, we shall have That is, 'The last term of a geometrical progression is equal to the product of the first term by that power of the ratio whose exponent is one less than the number of...

...c = bq=.aq1, d = cq = aq* from which it will be readily inferred, that a term of any rank whatever is equal to the first term multiplied by the ratio raised to a power, the exponent of which is one less than the number, which marks the place of this term. Let L designate...

...has n — 1 terms before it, is expressed by arn~1. Let I be this term , we then have the formula, by means of which we can obtain any term without being obliged to find all the terms which precede it. Hence, to find the last term of a progression, we have the following BULE. I. Raise the ratio to a...

...theory of Geometrical Progression is contained in the following propositions. , The Last Term. (186.) The last term of a Geometrical Progression, is equal to the first term X that power of the ratio which is expressed by the number of terms less one. Let a be the first term,...