A geometric sequence has first term 6 and common ratio 1.5. The sum of the first n terms of the sequence is 79.125. Find n.(please help me. Willing to give a medal)

Question

anonymous · Answer

thanks @cj49

campbell_st · Answer

the information is correct but the format of the fomula is incorrect... which will lead to an incorrect solution

you need 

$$79.125 = \frac{6( 1 - (1.5)^n}{(1 - 1.5)}$$

the common ratio needs to be in the same position in the numerator and denominator

anonymous · Answer

it says that I have to find n. and n= 5. but i dont know how to find that

campbell_st · Answer

ok... so you will need to use logarithms to find n. 

an alternative is guess and check...

campbell_st · Answer

@cj49 it is

cj49 · Answer

n = the number of terms that means there are total 5 terms

cj49 · Answer

6(1.5^n-1)
6(1.5^1)=2nd term
6(1.5^2)=3rd term
6(1.5^3)=4th term
6(1.5^4)=5th term

campbell_st · Answer

do if you do it correctly you get 

$$\frac{79.125 \times (1 - 1.5)}{6} =-7.59325$$

which means 

$$-1.5^n = -7.59325$$

divide both by -1 

$$1.5^n = 7.59325$$

take the log of both sides... doesn't matter which type of log

$$\ln(1.5^n) = \ln(7.59325)$$

or

$$n \ln(1.5) = \ln(7.59325)$$

so now solve for n

campbell_st · Answer

and you'll find n = 5...