(B) Let the $n^{th}$ term of the given $AP$ be $210$.Here,the first term $a = 21$.The common difference $d = 42 - 21 = 21$.We know the formula for the

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(B) Let the $n^{th}$ term of the given $AP$ be $210$.Here,the first term $a = 21$.The common difference $d = 42 - 21 = 21$.We know the formula for the $n^{th}$ term of an $AP$ is $a_n = a + (n - 1)d$.Substituting the values,we get $210 = 21 + (n - 1)21$.$210 = 21 + 21n - 21$.$210 = 21n$.$n = 210 / 21 = 10$.Therefore,the $10^{th}$ term of the $AP$ is $210$.

Class 10 Mathematics Arithmetic Progressions Mix Examples - Arithmetic Progressions

Medium

Which term of the $AP: 21, 42, 63, 84, \ldots$ is $210$?

A
$9$
B
$10$
C
$11$
D
$12$

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Class 10 Questions

Class 10

Mathematics Questions

Chapter

Arithmetic Progressions

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Mix Examples - Arithmetic Progressions

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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Find the number of terms in the finite $A.P.$ $7, 11, 15, \ldots, 107$.

Easy

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Which term of the $A.P.$ $83, 77, 71, \ldots$ is its first negative term (in $^{th}$)?

Easy

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The $n^{th}$ term of an $A.P.$ is given by $T_{n} = 7 - 3n$. Find the sum of the first $25$ terms of the $A.P.$

Medium

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Show that the sum of an $AP$ whose first term is $a,$ the second term is $b,$ and the last term is $c,$ is equal to $\frac{(a+c)(b+c-2a)}{2(b-a)}.$

Difficult

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Which term of the $AP: 21, 42, 63, 84, \ldots$ is $210$?

Similar Questions

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.

Find the number of terms in the finite $A.P.$ $7, 11, 15, \ldots, 107$.

Which term of the $A.P.$ $83, 77, 71, \ldots$ is its first negative term (in $^{th}$)?

The $n^{th}$ term of an $A.P.$ is given by $T_{n} = 7 - 3n$. Find the sum of the first $25$ terms of the $A.P.$

Show that the sum of an $AP$ whose first term is $a,$ the second term is $b,$ and the last term is $c,$ is equal to $\frac{(a+c)(b+c-2a)}{2(b-a)}.$

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