Question

In arithmetic progression first term is 3 and an =4an-1+3,n1 find the fourth term

Answer 1

I hope this helps you

Answer 2

$Given \: First \: term \:in \: A.P ( a = a_{1} ) = 3$

$and \: a_{n} = 4a_{(n-1)} + 3$

$i) a_{2} = 4a_{(2-1)} + 3 \\= 4a_{1} + 3 \\= 4\times 3 + 3 \\= 12 + 3\\= 15$

$ii) a_{3} = 4a_{(3-1)} + 3 \\= 4a_{2} + 3 \\= 4\times 15 + 3 \\= 60 + 3\\= 63$

$iii) Fourth \:term \\= a_{4} = 4a_{(4-1)} + 3 \\= 4a_{3} + 3 \\= 4\times 63 + 3 \\= 189 + 3\\= 192$

Therefore.,

$\red { Fourth \:term \: in \: given \:A.P } \green {= 192 }$

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