Answer with proof in attachment.
Express each ratio as a unit rate. Round to the nearest tenth or cent.
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Answer:
2097150
Step-by-step explanation:
<u>GIVEN :-</u>
- First term of G.P. = 6
- Forth term of G.P. = 384
<u>TO FIND :-</u>
- Sum of first 10 terms of the G.P.
<u>CONCEPT TO BE USED IN THIS QUESTION :-</u>
<em>Geometric Progression :-</em>
- It's a sequence in which the successive terms have same ratio.
- General form of a G.P. ⇒ a , ar , ar² , ar³ , ....... [where a = first term ; r = common ratio between successive terms]
- Sum of 'n' terms of a G.P. ⇒
.
<em>[NOTE :- </em> can also be the<em> formula for "Sum of n terms of G.P." because if you put 'r' there (assuming r > 0) you'll get negative value in both the numerator & denominator from which the negative sign will get cancelled from the numerator & denominator. </em><em>YOU'LL BE GETTING THE SAME VALUE FROM BOTH THE FORMULAES.</em><em>]</em>
<u>SOLUTION :-</u>
Let the first term of the G.P. given in the question be 'a' and the common ratio between successive terms be 'r'.
⇒ a = 6
It's given that <u>forth term</u> is 384. So from "General form of G.P." , it can be stated that :-
Divide both the sides by 6.
Sum of first 10 terms