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 answer:

s₂ =  30

Step-by-step explanation:

$$\begin{gathered} s_1=120 \\ n=10 \\ {s}_1=a_1+a_2+a_3+\dots +a_n \\ {d}_2=d_1-2 \\ {s}_1=10\mathrm{/}2\cdot (a_1+a_1+9\cdot d_1)=10\cdot a_1+45\cdot d_1=120 \\ {s}_2=10\mathrm{/}2\cdot [a_1+a_1+9\cdot (d_1-2)] \\ {s}_2=10\cdot a_1+45\cdot d_1-5\cdot 9\cdot 2 \\ {s}_2=s_1-5\cdot 9\cdot 2=120-5\cdot 9\cdot 2=30 \end{gathered}$$

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