Question

The 20th term of AP exceeds its 15th term by 10.find the common difference

Answer 1

Hope it would help you

Answer 2

$\large\underline{Given:-}$

• 20th term exceed 15th term by 10.

$\large\underline{To find:-}$

• find the common difference.

$\large\underline{Solutions:-}$

• $\: \: \: \: \: {a_n} \: \: = \: \: {a} \: + \: {(n \: - \: 1)} \: d$
• $\: \: \: \: \: {a_{20}} \: \: = \: \: {a} \: + \: {19d}$
• $\: \: \: \: \: {a_{15}} \: \: = \: \: {a} \: + \: {14d}$

»★Now,

✰ 20th term exceed 15th term by 10.

$\: \: \: \: \: \leadsto {a_{20}} \: - \: {a_{15}} \: \: = \: \: {10}$

$\: \: \: \: \: \leadsto {a} \: + \: {19d} \: - \: {({a} \: + \: {14d})} \: \: = \: \: {10}$

$\: \: \: \: \: \leadsto {a} \: + \: {19d} \: - \: {a} \: - \: {14d} \: \: = \: \: {10}$

$\: \: \: \: \: \leadsto {19d} \: - \: {14d} \: \: = \: \: {10}$

$\: \: \: \: \: \leadsto {5d} \: \: = \: \: {10}$

$\: \: \: \: \: \leadsto {d} \: \: = \: \: \frac{10}{5}$

$\: \: \: \: \: \leadsto {d} \: \: = \: \: {2}$

»★Hence, Common difference is 2.

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