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  4. If a + 1, 2a + 1, 4a - 1 are in arithmetic progression, then the value of a is

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Q. If $a + 1, 2a + 1, 4a - 1$ are in arithmetic progression, then the value of $a$ is

KEAMKEAM 2017Sequences and Series

Solution:

We have,
$a+1,2 \,a+1 ; 4\, a-1$ are in $A P$
$\therefore 2(2\, a+1)=(4 \,a-1)+(a+1)$
$[\because$ If $a, b, c$ are in $A P$, then $2 \,b=a+c]$
$\Rightarrow 4 a+2=5 \,a $
$\Rightarrow a=2$