(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

For each of the following $A.P.s$,find the $n^{th}$ term: $27, 22, 17, 12, \ldots$

Easy

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The angles of a triangle are in $AP$. The greatest angle is twice the least. Find all the angles of the triangle (in $^circ$).

Difficult

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The sum of three numbers in $A.P.$ is $21$. The product of the first and the third number exceeds the second number by $6$. Find those numbers.

Medium

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If the $2^{\text{nd}}$ term of an $AP$ is $13$ and the $5^{\text{th}}$ term is $25$,what is its $7^{\text{th}}$ term?

Medium

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Find the sum of the integers between $100$ and $200$ that are not divisible by $9$.

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

Similar Questions

For each of the following $A.P.s$,find the $n^{th}$ term: $27, 22, 17, 12, \ldots$

The angles of a triangle are in $AP$. The greatest angle is twice the least. Find all the angles of the triangle (in $^circ$).

The sum of three numbers in $A.P.$ is $21$. The product of the first and the third number exceeds the second number by $6$. Find those numbers.

If the $2^{\text{nd}}$ term of an $AP$ is $13$ and the $5^{\text{th}}$ term is $25$,what is its $7^{\text{th}}$ term?

Find the sum of the integers between $100$ and $200$ that are not divisible by $9$.

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