(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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Arithmetic Progressions

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Mix Examples - Arithmetic Progressions

Determine the $AP$ whose fifth term is $19$ and the difference of the eighth term from the thirteenth term is $20$.

Medium

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The ratio of the sums of first $n$ terms of two $A.P.s$ is $(5n - 3) : (7n + 2)$. Find the ratio of their $m^{th}$ terms.

Difficult

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For an $A.P.$,the $12^{th}$ term is $-13$ and the sum of its first $4$ terms is $24$. Find the sum of the first $10$ terms of the $A.P.$

Difficult

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For a given $A.P.$,the $5^{th}$ term is $30$ and the $12^{th}$ term is $65$. Find the sum of first $30$ terms of this $A.P.$

Medium

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Which term of the $A.P.$ $5, 15, 25, \ldots$ exceeds its $31^{st}$ term by $130$ (in $^{th}$)?

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

Determine the $AP$ whose fifth term is $19$ and the difference of the eighth term from the thirteenth term is $20$.

The ratio of the sums of first $n$ terms of two $A.P.s$ is $(5n - 3) : (7n + 2)$. Find the ratio of their $m^{th}$ terms.

For an $A.P.$,the $12^{th}$ term is $-13$ and the sum of its first $4$ terms is $24$. Find the sum of the first $10$ terms of the $A.P.$

For a given $A.P.$,the $5^{th}$ term is $30$ and the $12^{th}$ term is $65$. Find the sum of first $30$ terms of this $A.P.$

Which term of the $A.P.$ $5, 15, 25, \ldots$ exceeds its $31^{st}$ term by $130$ (in $^{th}$)?

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