Find 31 st term of an AP whose 11 th term is 38 and 16 th term is 73

1.	Find 31 st term of an AP whose 11 th term is 38 and 16 th term is 73
Answer» {tex}\\eqalign{ & {t_{31}} = a + 30d \\cr & = - 32 + 30(7) \\cr & = 178 \\cr} {/tex} {tex}\\eqalign{ & Given\\,\\,that\\,:{t_{11}} = 38 \\cr & {t_{16}} = 73 \\cr & Let\\,first\\,term\\,be\\,a\\,and\\,common\\,difference\\,is\\,d \\cr & a + 10d = 38\\,\\,\\,\\,\\,\\,eq.\\left( 1 \\right) \\cr & a + 15d = 73\\,\\,\\,\\,\\,\\,\\,eq.(2) \\cr & eqs.(1)\\, - (2) \\cr & - 5d = - 35 \\cr & d = 7 \\cr & so\\,from\\,(1) \\cr & a = - 32 \\cr & {t_{38}} = a + 37d \\cr & = - 32 + 37(7) \\cr & = 227 \\cr & \\cr} {/tex} 178

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