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Show that the progression -11,-7,-3,1,5,…, 161 is an AP. How many tems does it have ?

Answer» we have
(-7) - (-11) = (-7 +11) = 4, (-3) - (-7) = ( -3+7) =4
1-(-3) = ( 1+3) =4 and ( 5-1) =4
{ (-7) -(-11)}= { (-3) - (-7)} = {1-(-3)} = ( 5-1) =4, which is contant .
So, the given progression is an AP in which a = -11 and d =4 let it have n terms. then ,
` T_(n)= 161 Rightarrow a+ ( n-1) d = 161 `
` Rightarrow (-11) + ( n-1) xx 4 = 161`
` Rightarrow 4n = 176 Rightarrow n= 44 `
` T_(44) =161` and hence there are 44 terms in the given AP .


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