(D) The formula for the sum of the first $n$ terms of an $A.P.$ is given by $S_{n} = \frac{n}{2} [2a + (n - 1)d]$.Given $S_{10} = 50$,$n = 10$,and $a

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(D) The formula for the sum of the first $n$ terms of an $A.P.$ is given by $S_{n} = \frac{n}{2} [2a + (n - 1)d]$.Given $S_{10} = 50$,$n = 10$,and $a = 0.5$.Substituting these values into the formula:$50 = \frac{10}{2} [2(0.5) + (10 - 1)d]$$50 = 5 [1 + 9d]$Dividing both sides by $5$:$10 = 1 + 9d$$9 = 9d$$d = 1$.

Class 10 Mathematics Arithmetic Progressions Mix Examples - Arithmetic Progressions

Medium

For a given $A.P.$,$S_{10} = 50$ and $a = 0.5$. Then,$d = \ldots \ldots \ldots . .$

A
$4$
B
$3$
C
$2$
D
$1$

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Class 10

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Arithmetic Progressions

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Mix Examples - Arithmetic Progressions

Find the $20^{\text{th}}$ term of the $AP$ whose $7^{\text{th}}$ term is $24$ less than the $11^{\text{th}}$ term,first term being $12$.

Medium

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The $20^{th}$ term of the $A.P.$ $1, 11, 21, \ldots$ is........

Easy

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The ratio of the sums of first $n$ terms of two $A.P.s$ is $\frac{4n+3}{5n-7}$. Find the ratio of $15^{th}$ terms of the $A.P.s$.

Difficult

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For an $A.P.$,the $5^{th}$ term is $30$ and the $12^{th}$ term is $100$. Find the sum of the first $20$ terms of the $A.P.$

Medium

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For the finite $A.P.$ $12, 21, 30, \ldots, 363,$ find the $12^{th}$ term from the end.

Medium

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For a given $A.P.$,$S_{10} = 50$ and $a = 0.5$. Then,$d = \ldots \ldots \ldots . .$

Similar Questions

Find the $20^{\text{th}}$ term of the $AP$ whose $7^{\text{th}}$ term is $24$ less than the $11^{\text{th}}$ term,first term being $12$.

The $20^{th}$ term of the $A.P.$ $1, 11, 21, \ldots$ is........

The ratio of the sums of first $n$ terms of two $A.P.s$ is $\frac{4n+3}{5n-7}$. Find the ratio of $15^{th}$ terms of the $A.P.s$.

For an $A.P.$,the $5^{th}$ term is $30$ and the $12^{th}$ term is $100$. Find the sum of the first $20$ terms of the $A.P.$

For the finite $A.P.$ $12, 21, 30, \ldots, 363,$ find the $12^{th}$ term from the end.

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