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  4. Let a1, a2, a3, a4 are positive numbers which are consecutive terms in a geometric progression. If a1+a2=10 and a3+a4=40, then the value of (a1+a4) equals

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Q. Let $a_1, a_2, a_3, a_4$ are positive numbers which are consecutive terms in a geometric progression. If $a_1+a_2=10$ and $a_3+a_4=40$, then the value of $\left(a_1+a_4\right)$ equals

Sequences and Series

Solution:

$ a_1(1+r)=10$ ....(1)
$a_1 r ^2(1+r)=40$ ...(2)
$\therefore a_1=\frac{10}{3}, r=2 .$