Sequences & Series
AP Terms in GP — Sum of First 20 Terms
nta_pyq_2024_jan
Grade 11
Question:
Let $2^{\text{nd}},8^{\text{th}}$ and $44^{\text{th}}$ terms of a non-constant A.P. be respectively the $1^{\text{st}},2^{\text{nd}}$ and $3^{\text{rd}}$ terms of a G.P. If the first term of the A.P. is 1, then the sum of first 20 terms is equal to
Step-by-Step Solution
Key Concept: AP: $a_1=1$, general term $1+(n-1)d$. Terms: $T_2=1+d$, $T_8=1+7d$, $T_{44}=1+43d$ in GP. $(1+7d)^2=(1+d)(1+43d)$.
$d=5$. $S_{20}=10(2+95)=970$.
Correct Answer: 4