(B) The formula for the sum of $n$ terms of an $A.P.$ when the first term $a$ and the last term $l$ are known is given by:$S_n = \frac{n}{2}(a + l)$Gi

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(B) The formula for the sum of $n$ terms of an $A.P.$ when the first term $a$ and the last term $l$ are known is given by:$S_n = \frac{n}{2}(a + l)$Given:First term $a = 5$Last term $l = 45$Sum of terms $S_n = 500$Substituting the values into the formula:$500 = \frac{n}{2}(5 + 45)$$500 = \frac{n}{2}(50)$$500 = 25n$$n = \frac{500}{25}$$n = 20$Therefore,there are $20$ terms in the $A.P.$

Class 10 Mathematics Arithmetic Progressions Mix Examples - Arithmetic Progressions

Easy

The first term of a finite $A.P.$ is $5$ and its last term is $45$. If the sum of all the terms is $500$,there are $\ldots$ terms in the $A.P.$

A
$10$
B
$20$
C
$30$
D
$50$

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Class 10 Questions

Class 10

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Arithmetic Progressions

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Mix Examples - Arithmetic Progressions

Find the sum of those integers between $1$ and $500$ which are multiples of $2$ as well as of $5$.

Difficult

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The $n^{th}$ term of an $A.P.$ is given by $T_{n} = 8n + 3$. Find the sum of the first $n$ terms of the $A.P.$

Medium

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Which term of the $A.P.$ $108, 103, 98, \ldots$ is its first negative term?

Difficult

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Which term of the $A.P.$ $53, 48, 43, \ldots$ is its first negative term? Find that term.

Medium

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The $8^{th}$ term of an $A.P.$ is $31$ and its $15^{th}$ term exceeds its $11^{th}$ term by $16$. Find the $A.P.$ and also its $20^{th}$ term.

Medium

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The first term of a finite $A.P.$ is $5$ and its last term is $45$. If the sum of all the terms is $500$,there are $\ldots$ terms in the $A.P.$

Similar Questions

Find the sum of those integers between $1$ and $500$ which are multiples of $2$ as well as of $5$.

The $n^{th}$ term of an $A.P.$ is given by $T_{n} = 8n + 3$. Find the sum of the first $n$ terms of the $A.P.$

Which term of the $A.P.$ $108, 103, 98, \ldots$ is its first negative term?

Which term of the $A.P.$ $53, 48, 43, \ldots$ is its first negative term? Find that term.

The $8^{th}$ term of an $A.P.$ is $31$ and its $15^{th}$ term exceeds its $11^{th}$ term by $16$. Find the $A.P.$ and also its $20^{th}$ term.

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