Solver Arithmetic Progression (AP) Solver
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Algebra: Sequences of numbers, series and how to sum them
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==section input This solver will display the first few terms of an Arithmetic Progression, and the sum of the first n terms. Assuming standard notation so that the terms in the Arithmetic Progression are: a, a+d, a+2d, a+3d , ... Enter the first term a *[input a=1] Enter the common difference d *[input d=1] Enter the number of terms to sum n *[input n=10] ==section solution The first few terms of this AP are: a=*[assign term1=$a]$term1, a+d=*[assign term2=($a)+($d)]$term2, a+2d=*[assign term3=($a)+2($d)]$term3, a+3d=*[assign term4=($a)+3($d)]$term4, ... or, just: $term1, $term2, $term3, $term4, ... The Sum of the first n terms is given by: {{{ S[n]= (n/2)(2a+(n-1)d) }}} So substituting a=$a, d=$d and n=$n gives: {{{ S[$n]= ($n/2)(2($a)+($n-1)$d) = *[assign sum=(($n)/2)(2($a) + (($n)-1)($d))]$sum }}} ==section output term1 term2 term3 term4 sum ==section check a=8 d=-4 n=15 term1=8 term2=4 term3=0 term4=-4 sum=-300
