Sequences & Series
AP — Sum and Ratio of Terms
nta_pyq_2024_jan
Grade 11
Question:
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:
Step-by-Step Solution
Key Concept: $S_{10}=5(2a+9d)=390\Rightarrow2a+9d=78$. $t_{10}/t_5=(a+9d)/(a+4d)=15/7\Rightarrow7a+63d=15a+60d\Rightarrow8a=3d$. Solve to get $a$ and $d$.
$a=3,d=8$. $S_{15}-S_5=790$.
Correct Answer: 3