9758/2020/P1/Q08

(a) The 1 st term of an arithmetic series is 4 and the 5 th term is 10.

(i) Find the 30 th term of this series.

[2]

(ii) Find the sum of the 21 st term to the 50 th term inclusive of this series.

[3]

(b) The 1st term of a geometric series is 4 and the 5 th term is $1.6384$ where the common ratio is positive.

(i) Find the sum to infinity of this series.

[2]

(ii) Given that the sum of the first $n$ terms is greater than $19.6$, show that

$$0.8^{n}<0.02 \text {. }$$

Hence find the smallest possible value of $n$.

[5]