## Eyad 3 years ago Geometric sequence of positive terms in which its first term equal 4 times its third term and the sum of its second term ,fifth term is 36 ..Find The G.s .....

1. Ceriona

so, if the terms are labled \[n _{1}\] for the first term \[n _{_{2}}\] for the second, and so on. Does \[n _{1} = 4n _{3} + n _{2}\] or\[n _{1} = 4(n _{3} + n _{2})\]

can't we say a=first term where a=4T3 ,a=4(ar^2)----->(1) T2+T5=36 ,ar+ar^4=36 , ar(1+r^3)=36------->(2) and deal with these two equations ?

3. Ceriona

ok, that works

4. Ceriona

ok, so this is what I got|dw:1337900631418:dw|

5. Ceriona

|dw:1337900769253:dw|

6. Ceriona

Can you follow what I did, or is my writing a little to hard to read?

no , i can follow :)

But how come the first term be fraction ,I think something is going wrong :/

9. Ceriona

The first term isn't a fraction. The first term is "a" which is 64. "r" is the number we're multiplying each term by to get the next.

Oh,sry i read it wrong ,ty :)

11. Ceriona

So first term is 64, second is 32, third is 16, fourth is 8, fifth is 4 ..... 4 * 16 = 64 (first term equal to 4 times third term) and 32 + 4 = 36 (second term plus fifth term equals 36). It fits both of the original equations.