# Given the first term and the common difference of an arithmetic sequence. Find the first five terms and explicit formula: a1= -38, d=-100

Given the first term and the common difference of an arithmetic sequence. Find the first five terms and explicit formula: a1= -38, d=-100
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Lorenzo Aguilar
To calculate the consecutive terms just add d to ${a}_{1}$, so you get:
${a}_{2}={a}_{1}+r=-38+\left(-100\right)=-138$
${a}_{3}=a-2-100=-138-100=-238$
and so on

To find the formula just substitute ${a}_{1}$ and r in ${a}_{n}={a}_{1}+\left(n-1\right)r$

${a}_{n}=-38-100\left(n-1\right)=-38-100n+100=62-100n$
${a}_{1}=-38,{a}_{2}=-138,{a}_{3}=-238,{a}_{4}=-338,{a}_{5}=-438$