Sequences And Series Question 3
Question 3 - 2024 (01 Feb Shift 2)
Let $S_{n}$ denote the sum of the first $n$ terms of an arithmetic progression. If $S_{10}=390$ and the ratio of the tenth and the fifth terms is $15: 7$, then $S_{15}-S_{5}$ is equal to:
(1) 800
(2) 890
(3) 790
(4) 690
Show Answer
Answer (3)
Solution
$\mathrm{S}_{10}=390$
$\frac{10}{2}[2 \mathrm{a}+(10-1) \mathrm{d}]=390$
$\Rightarrow 2 \mathrm{a}+9 \mathrm{~d}=78 \ldots(1)$
$\frac{t_{10}}{t_{5}}=\frac{15}{7} \Rightarrow \frac{a+9 d}{a+4 d}=\frac{15}{7} \Rightarrow 8 a=3 d$.
From (1) & (2), $a=3 & d=8$
$S_{15}-S_{5}=\frac{15}{2}(6+14 \times 8)-\frac{5}{2}(6+4 \times 8)$
$=\frac{15 \times 118-5 \times 38}{2}=790$
