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InterviewSolution
| 1. |
The 19th term of a.p is equal to three times its 6th term is 19 find the a.p |
| Answer» Let the first term of the A.P. be \'a\'.and the common difference be \'d\'.19th term of the A.P., t19 = a + (19 - 1)d = a + 18d6th term of the A.P., t6 = a + (6 - 1)d = a + 5d9th term of the A.P., t9 = a + (9 - 1)d = a + 8dt19 = 3t6{tex}\\Rightarrow{/tex}a + 18d = 3(a + 5d){tex}\\Rightarrow{/tex}a + 18d = 3a\xa0+ 15d{tex}\\Rightarrow{/tex}18d - 15d = 3a - a{tex}\\Rightarrow{/tex}3d = 2a{tex}\\therefore \\mathrm { a } = \\frac { 3 \\mathrm { d } } { 2 }{/tex}t9 = 19{tex}\\Rightarrow \\frac { 3 \\mathrm { d } } { 2 } + 8 \\mathrm { d } = 19{/tex}{tex}\\Rightarrow \\frac { 3 d + 16 d } { 2 } = 19{/tex}{tex}\\Rightarrow \\frac { 19 \\mathrm { d } } { 2 } = 19{/tex}{tex}\\Rightarrow{/tex}\xa0d = 2{tex}\\Rightarrow{/tex}a = 3t2\xa0= 3 + (2 - 1)2 = 5t3\xa0= 3 + (3 - 1)2 = 7The series will be 3, 5, 7...... | |