The sum of the first $10$ terms of an AP is $230$. If the first term is $5$, what is the common difference?

Step-by-step solution

1. Use the sum formula: $S_n=\frac{n}{2}\left[2a+(n-1)d\right]$.
2. Substitute $S_{10}=230$, $n=10$, $a=5$:
3. $230=\frac{10}{2}\left[2\times 5+(10-1)d\right]=5\left[10+9d\right]$.
4. Divide both sides by $5$: $46=10+9d$.
5. Subtract $10$: $36=9d$.
6. Divide by $9$: $d=4$.

Concept tested: sum of n terms

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