Sequences & Series
AP and GP Mixed — Arithmetic Mean
nta_pyq_2024_jan
Grade 11
Question:
Let $3,a,b,c$ be in A.P. and $3,a-1,b+1,c+9$ be in G.P. Then the arithmetic mean of $a,b$ and $c$ is:
Step-by-Step Solution
Key Concept: From AP: $a=3+d$, $b=3+2d$, $c=3+3d$. GP condition: $(a-1)^2=(3)(b+1)$ and $(b+1)^2=(a-1)(c+9)$. Solve for $d$.
$d=4$: $a=7,b=11,c=15$. AM $=11$.
Correct Answer: 4