vballa15ei
2022-09-14
Answered

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

Answered 2022-09-15
Author has **18** answers

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 $\{6,10,15,21,28,...........\}$

${a}_{2}={a}_{1}+1+3=6+1+3=10$

${a}_{3}={a}_{2}+2+3=10+2+3=15$

${a}_{4}={a}_{3}+3+3=15+3+3=21$

${a}_{5}={a}_{4}+4+3=21+4+3=28$

Hence first five term are $\{6,10,15,21,28,...........\}$

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