The sum

The sum of the first 10 members of the arithmetic sequence is 120. What will be the sum if the difference is reduced by 2?

Correct result:

s2 =  30

Solution:

s1=120 n=10  s1=a1+a2+a3+…+an  d2=d1−2  s1=10/2⋅ (a1+a1+9⋅ d1)=10⋅ a1+45⋅ d1=120 s2=10/2⋅ [a1+a1+9⋅ (d1−2)] s2=10⋅ a1+45⋅ d1−5⋅ 9⋅ 2  s2=s1−5⋅ 9⋅ 2=120−5⋅ 9⋅ 2=30

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