Question

Identify a3 of this sequence: 0.25, 0.5, 0.75, 1, 1.25, 1.5, …

a3 =

Answer 1

Answer:

Next 3 are 1.75,2.00,2.25

Answer 2

$Given \: sequence \: 0.25, 0.5, 0.75 , 1,\\ 1.25,1.5 ,\ldots$

$Here, First \:term (a = a_{1}) = 0.25$

$a_{2} = 0.5$

$i ) a_{2} - a_{1} \\= 0.5 - 0.25 \\= 0.25 \: --(1)$

$ii ) a_{3} - a_{2} \\= 0.75 - 0.5 \\= 0.25 \: --(2)$

$From\: (1) \: and \: (2)$

$\blue{a_{2} - a_{1} = a_{3} - a_{2} = 0.25 }$

$\therefore Given \: is \: in \: Arithmetic \: progression$

$Common \: difference (d) = 0.25$

$Here, a = 0.25, d = 0.25$

$\red{ n^{th} \: term \: (a_{n}) } \\= a + (n-1)d \\= 0.25 + (n-1) \times 0.25\\= 0.25[ 1 + n - 1 ] \\= 0.25n$

Therefore.,

$\red{ n^{th} \: term \: (a_{n}) } \green { = 0.25n }$

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