Find a,b,and c such that the Nos a,7,6,23,c in AP

1.	Find a,b,and c such that the Nos a,7,6,23,c in AP
Answer» {tex}a, 7, b, 23{/tex} and {tex}c{/tex} are in A.P.Let the common difference be d.{tex}a + d = 7{/tex} ....(i){tex}a + 3d = 23{/tex} ....(ii)From (i) and (ii), we get{tex}2d = 16{/tex}{tex}d = 8{/tex}Put d = 8 in (1) we get{tex}a + 8 = 7{/tex}{tex}a = -1{/tex}{tex}b = a + 2d{/tex}{tex}b = - 1{/tex} + 2 {tex}\\times{/tex}\xa08or,{tex} b = - 1 + 16{/tex}or, {tex}b = 15{/tex}{tex}c = a + 4d{/tex}= - 1 + 4 {tex}\\times{/tex}\xa08= - 1 + 32{tex}c = 31{/tex}{tex}\\therefore{/tex}\xa0{tex}a = - 1,b = 15, c =31{/tex}

Discussion