(A) Since $a, 7, b, 23, c$ are in $AP$,the common difference $d$ is constant.$d = 7 - a = b - 7 = 23 - b = c - 23$.From $b - 7 = 23 - b$,we get $2b =

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(A) Since $a, 7, b, 23, c$ are in $AP$,the common difference $d$ is constant.$d = 7 - a = b - 7 = 23 - b = c - 23$.From $b - 7 = 23 - b$,we get $2b = 30$,so $b = 15$.Using $7 - a = b - 7$,substitute $b = 15$:$7 - a = 15 - 7 = 8$,which gives $a = 7 - 8 = -1$.Using $c - 23 = 23 - b$,substitute $b = 15$:$c - 23 = 23 - 15 = 8$,which gives $c = 8 + 23 = 31$.Thus,$a = -1, b = 15, c = 31$.

Class 10 Mathematics Arithmetic Progressions Mix Examples - Arithmetic Progressions

Medium

Find $a, b$ and $c$ such that the following numbers are in $AP : a, 7, b, 23, c$.

A
$-1, 15, 31$
B
$-1, 14, 30$
C
$-2, 16, 30$
D
$-1, 11, 31$

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Arithmetic Progressions

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Mix Examples - Arithmetic Progressions

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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Find the value of the middle most term$(s)$ of the $AP:$ $-11, -7, -3, \ldots, 49$.

Difficult

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Four numbers in increasing order form an $A.P.$ The sum of those numbers is $32$ and the ratio of the product of extremes to the product of means is $7: 15$. Find those numbers.

Medium

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Which of the following sequences is an $A.P.$?

Medium

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For an $A.P.$,the $2^{nd}$ term is $2$ and the $7^{th}$ term is $22$. Find the sum of the first $30$ terms of the $A.P.$

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Find $a, b$ and $c$ such that the following numbers are in $AP : a, 7, b, 23, c$.

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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 $A.P.s$.

Find the value of the middle most term$(s)$ of the $AP:$ $-11, -7, -3, \ldots, 49$.

Four numbers in increasing order form an $A.P.$ The sum of those numbers is $32$ and the ratio of the product of extremes to the product of means is $7: 15$. Find those numbers.

Which of the following sequences is an $A.P.$?

For an $A.P.$,the $2^{nd}$ term is $2$ and the $7^{th}$ term is $22$. Find the sum of the first $30$ terms of the $A.P.$

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