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Home / \( 145 = \frac{10}{2} (2 \times 5 + 9d) \)

\( 145 = \frac{10}{2} (2 \times 5 + 9d) \)

February 22, 2026

$145 = \frac{10}{2} (2 \times 5 + 9d)$

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The sum of the first 10 terms of an arithmetic sequence is 145. If the first term is 5, what is the common difference?
Sum formula: \( S_n = \frac{n}{2} (2a + (n-1)d) \)
Here, \( S_{10} = 145 \), \( a = 5 \), \( n = 10 \)
\( 145 = 5 (10 + 9d) \)
\( 145 = 50 + 45d \)
\( 95 = 45d \)

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