Sequences And Series Question 1
Question 1 - 2024 (01 Feb Shift 1)
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 :
(1) -4
(2) -1
(3) 13
(4) 11
Show Answer
Answer (4)
Solution
$3, a, b, c \rightarrow$ A.P $\quad \Rightarrow 3,3+d, 3+2 d, 3+3 d$
$3, a-1, b+1, c+9 \rightarrow$ G.P $\Rightarrow 3,2+d, 4+2 d, 12+3 d$
$a=3+d \quad(2+d)^{2}=3(4+2 d)$
$b=3+2 d \quad d=4,-2$
$c=3+3 d$
If $d=4 \quad$ G.P $\Rightarrow 3,6,12,24$
$a=7$
$b=11$
$c=15$
$\frac{a+b+c}{3}=11$
