For what value of p,2p+1,13p ,5p-3 are AP

1.	For what value of p,2p+1,13p ,5p-3 are AP
Answer» let the three consecutive terms of AP be {tex}a_1,a_2,a_3{/tex}where\xa0{tex}a_1=(2p+1),a_2=13,a_3=(5p-3){/tex}we know that difference between any two consecutive terms of an AP is equal{tex}\\therefore{a_2} - {a_1} = {a_3} - {a_2}{/tex}{tex} \\Rightarrow 13 - (2p + 1) = (5p - 3) - 13{/tex}{tex} \\Rightarrow 12 - 2p = 5p - 16{/tex}{tex} \\Rightarrow 7p = 28{/tex}{tex} \\Rightarrow p = 4{/tex}

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