Question
Seventh term of geometric series is 64 and sum of its 10 terms is 1023. Find its 15th term.
Answers
Reiny
You MUST know the definitions.
Seventh term of geometric series is 64
---> ar^6 = 64 **
sum of its 10 terms is 1023
---> a(r^10 - 1)/(r-1) = 1023 ***
divide *** by ** , the a will cancel
(r^10 - 1)/(r^6(r-1)) = 1023/64
64r^10 - 64 = 1023r^7 - 1023r^6 = 1023r^6(r-1)
took a "wild guess" at r = 2 , by knowing that 2^10 = 1024
LS = 64(1024)-64 = 65472
RS = 1023(64) = 65472
if r = 2, the a = 1 form ***
term15 = ar^14
= 16384
Seventh term of geometric series is 64
---> ar^6 = 64 **
sum of its 10 terms is 1023
---> a(r^10 - 1)/(r-1) = 1023 ***
divide *** by ** , the a will cancel
(r^10 - 1)/(r^6(r-1)) = 1023/64
64r^10 - 64 = 1023r^7 - 1023r^6 = 1023r^6(r-1)
took a "wild guess" at r = 2 , by knowing that 2^10 = 1024
LS = 64(1024)-64 = 65472
RS = 1023(64) = 65472
if r = 2, the a = 1 form ***
term15 = ar^14
= 16384