Sequences & Series
Arithmetico-Geometric Progression
nta_pyq_2023_apr
Grade 11
Question:
Let $a_1,a_2,2,a_3,a_4$ be in an AGP with common ratio 2 and sum $\frac{49}{2}$. Then $a_4$ is equal to ______________
Step-by-Step Solution
Key Concept: Terms: $a_1,2a_1+d,2(a_1+2d),8(a_1+3d),16(a_1+4d)$... Actually in AGP with first AP term $a_1$, common difference $d$, GP ratio 2: $k$th term $=(a_1+(k-1)d)\cdot2^{k-1}$. Third term $=2$.
$a_1=0,d=\frac{1}{4}$. $a_4=(4d)\cdot2^4=1\cdot16=16$.
Correct Answer: 16