Geometric Progression

Ipsita

The sum of an infinite GP is 16, its second term is 4. Find the first term

skeeter

MHF Helper
$\dfrac{a_1}{1-r} = 16$

$a_1 \cdot r = 2$

solve the system of equations ... note there are two possible solutions

Ipsita

Second term should be 4 right? If i solve it then it comes something as follows-
a1 = 16 (1-r) and a1= 4/r
This implies 16(1-r) = 4/r and the equation thus formed is r^2-16r+4 = 0. Now middle term is not possible here and the answers are given as 2, 6, 8 and 1/2. Then where am I wrong?

skeeter

MHF Helper
sorry, I saw 2nd term as 2 for some reason.

to correct ...

$a_1 \cdot r = 4 \implies r = \dfrac{4}{a_1}$

$\dfrac{a_1}{1 - \frac{4}{a_1}} = 16$

$\dfrac{a_1^2}{a_1 - 4} = 16$

$a_1^2 - 16a_1 + 64 = 0$

solve the quadratic for $a_1$

Ipsita

Yeah now it can easily be solved. But where was my mistake can you point me out?