Given the first term and the common difference of an arithmetic sequence how do you find the first five terms and explicit formula: a1 = 35, d=4?

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Answer 1 · 2015-07-17T20:04:26

The explicit formula for the sequence is $color(red)( a_n = 4n+31)$ , and the first five terms are $color(red)( 35,39,43,47,51)$ .

We know that the common difference $d = 4$ .

The general formula for an arithmetic sequence is

$a_n = a_1 + (n-1)d$ .

So, for your sequence, the general formula is

$a_n = 35 + 4(n-1) = 35 +4n-4$

$a_n = 4n+31$

$a_1 = 35$

$a_2 = 4×2+31 = 8+31 = 39$

$a_3 = 4×3+31 = 12+31 = 43$

$a_4 = 4×4+31 = 16+31= 47$

$a_5= 4×5+31 = 20+31 = 51$

The first five terms are $35,39,43,47,51$ .