Question

Q.17 If p – 1, p + 3, 3p – 1 are in AP, then p is equal to *

1 point

4

-4

2

-2

​

Answer 1

We know that,

If a,b,c are in A.P. then,

$\sf{2b = a + c}$

Here,

• a = p – 1

• b = p + 3

• c = 3p – 1

Substitute the values.

$\dashrightarrow\sf{2(p + 3) = p - 1 + 3p - 1}$

$\dashrightarrow\sf{2p + 6 = 4p - 2}$

$\dashrightarrow\sf{2p - 4p = - 2 - 6}$

$\dashrightarrow\sf{ - 2p = - 8}$

$\dashrightarrow\sf{2p = 8}$

$\dashrightarrow\textsf{\textbf{p = 4}}$

Hence, Value Of p = 4 [Option A].

Answer 2

$\rm{GIVEN:} \\ \\ </p><p></p><p> \rm{P-1, \: P+3, \: 3P-1 \: \: \: \: \: \: \: \: \: \implies Are \: in \: AP} \\ \\ </p><p></p><p> \rm{SOLUTION } \\ \\ </p><p></p><p> \rm{2b = a + c \: \: \: \: \: \: \: \implies(1)} \\ \\ </p><p></p><p> \rm{a = P-1}</p><p> \\ \\ </p><p> \rm{b = P+3} \\ \\ </p><p></p><p> \rm{c = 3P-1} \\ \\ </p><p></p><p>$

$\rm{SUBSTITUTE \: IN\: 1}$

$\rm2(P+3) = (P-1) + (3P-1)$

$\rm{4P + 6 = 4P - 2} \\ \\ </p><p></p><p></p><p> \rm{4P- 4P + 6 = -2} \\ \\ </p><p></p><p></p><p> \rm{= P - 2 + 6} \\ \\ </p><p></p><p></p><p> \rm{= P - 4} \\ \\ </p><p></p><p></p><p> \rm{4 = P}$

$\rm \boxed{P \: = 4}$

$\huge\rm \underline{HENCE \: PROVED}$