Question

first term of an arithmetic sequence is f and common difference d
5 times 5th term is equal to 10 times 10th term write the statement algebraically?​

Answer 1

Answer:

10 + 10 = 20

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Answer 2

Given :—
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first term = f

common difference = d
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$\\ \sf \qquad \: 5(fifth \: term) = 10(tenth \: term) \\ \\ \implies 5(f_5) = 10(f_{10}) \\ \\ \implies 5(f + 4d) = 10(f + 9d) \\ \\ \implies 5f + 20d = 10f + 90d \\ \\ \implies 10f - 5f = 20d - 90d \\ \\ \implies 5f = - 70d \\ \\ \implies f = - \frac{70}{5} d \\ \\ \implies f = - \frac{ \cancel{70} \: {}^{14} }{ \cancel{5} \: _1} d \\ \\ \implies f = - 14d$

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ADDITIONAL INFORMATION
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$\underline{\boxed{\bf{Arithmetic \: Progression}}}$
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In a sequence, if the difference between two consecutive terms is same then the sequence is known as an A.P.
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The first term is known as " a " .

The common difference is known as " d " .

The 'nth term' is given by : $\Large\sf\red{\underline{\fbox{\green{a_n = [a + (n - 1)d]}}}}$

The sum of 'n' terms is given by : $\Large\sf\red{\underline{\fbox{\green{S_n = \frac{n}{2} [2a + (n - 1)d]}}}}$
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