An arithmetic series has first term $a$ and common difference $d$, where $a$ is non-zero.

Question

An arithmetic series has first term $a$ and common difference $d$, where $a$ is non-zero. The $8$th, $4$th and $2$nd term of the arithmetic series are the first three consecutive terms of a geometric series respectively. It is also given that the terms of the arithmetic series are increasing. Show that $a = d$.[4] It is given that the sum of the first $20$ terms of the arithmetic series is $630$. Find the value of $a$.[2] Hence find the exact sum of the first $10$ terms of the geometric series.[3] Give a reason why the geometric series converges and find the sum to infinity of this series.[2]

Accepted Answer

(i) $a=d$ (ii) $a=3$ (iii) $\dfrac{3069}{64}$ (iv) The series converges because $|r|<1$, and $S_\infty=48$

2024 MI PRU1 Q8

2024 MI PRU1 Q8

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