# How do you find the first five terms given a_1=6 and a_(n+1)=a_n+n+3?

How do you find the first five terms given ${a}_{1}=6$ and ${a}_{n+1}={a}_{n}+n+3$?
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Maggie Tanner
As ${a}_{n+1}={a}_{n}+n+3$
${a}_{2}={a}_{1}+1+3=6+1+3=10$
${a}_{3}={a}_{2}+2+3=10+2+3=15$
${a}_{4}={a}_{3}+3+3=15+3+3=21$
${a}_{5}={a}_{4}+4+3=21+4+3=28$
Hence first five term are $\left\{6,10,15,21,28,...........\right\}$