Question

The value of p for which (2p + 1) , 10 and (5p + 5) are three consecutive terms of an AP is​

Answer 1

Given:

• 2p+1 , 10 and 5p+5 are in AP .

To find :

• The value of P

Solution:

As we know that , in AP :

• b-a = c-b

=> 2b= a+c

Here ,

• a = 2p+1 , • b = 10 and c= 5p+5

=> 2(10)=2p+1+5p+5

=> 20= 7p+6

=> 14= 7p

=> p = 14/7

=> p = 2

Hence, the value of p is 2.

Answer 2

$\huge \underline{ \underline{ \bf \purple{Solution :}}}$

As we know in an A.P

$\longrightarrow \: \sf b - a = c - b \\ \\ \longrightarrow \: \sf2b = a + c$

Here

• a = 2p + 1
• b = 10
• c = 5p + 5

Substitute values in formula

$\longrightarrow \: \sf 2(10) = 2p + 1 + 5p + 5 \\\\ \longrightarrow \: \sf20 = 7p + 6 \\\\ \longrightarrow \: \sf7p = 20 - 6 \\\\ \longrightarrow \: \sf7p = 14 \\\\ \longrightarrow \: \sf p = \frac{14}{7} \\ \\\large\longrightarrow \: \underline{\boxed{\sf \green{ p = 2}}}$