The first term of a convergent geometric progression is $3$. The sum of the first five terms of th

Question

The first term of a convergent geometric progression is $3$. The sum of the first five terms of the progression is twice the sum of the first ten terms. Find the sum to infinity of the progression. The twelfth term of an arithmetic progression is $52$ and the sum of the first eighteen terms is $756$. If the $n$th term of the progression is more than $2000$, find the least possible value of $n$.

Accepted Answer

(a) $S_\infty=\dfrac{3\sqrt[5]{2}}{1+\sqrt[5]{2}}\approx1.60$ (3 s.f.) (b) $n=500$

Sequence and Series - Problems involving inequalities

Sequence and Series - Problems involving inequalities

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