In a GP 72+144

In a GP, the sum of the 2nd and fifth terms is 72, and the sum of the 3rd and 6th terms is 144. Find the common ratio, find the first term, and find the sum of the first six terms

Correct answer:

q =  2
a₁ =  4
s₆ =  252

Step-by-step explanation:

$$\begin{gathered} s_{25}=72 \\ {s}_{36}=144 \\ {a}_1\cdot (q+q^4)=s_{25} \\ {a}_1\cdot (q^2+q^5)=a_1\cdot q(q+q^4)=s_{36} \\ q\cdot s_{25}=s_{36} \\ q=s_{36}/s_{25}=144/72=2 \end{gathered}$$

$a_1=\frac{s_{25}}{q+q^4}=\frac{72}{2+2^4}=4$

$s_6=a_1\cdot (1+q+q^2+q^3+q^4+q^5)=4\cdot (1+2+2^2+2^3+2^4+2^5)=252$

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