(A) The given $A.P.$ is $2, -2, -6, -10, \ldots$Here,the first term $a = 2$.The common difference $d = a_2 - a_1 = -2 - 2 = -4$.The formula for the $n

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(A) The given $A.P.$ is $2, -2, -6, -10, \ldots$Here,the first term $a = 2$.The common difference $d = a_2 - a_1 = -2 - 2 = -4$.The formula for the $n^{th}$ term of an $A.P.$ is $a_n = a + (n - 1)d$.To find the $20^{th}$ term $(n = 20)$:$a_{20} = 2 + (20 - 1)(-4)$$a_{20} = 2 + (19)(-4)$$a_{20} = 2 - 76$$a_{20} = -74$.Therefore,the $20^{th}$ term is $-74$.

Class 10 Mathematics Arithmetic Progressions Mix Examples - Arithmetic Progressions

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The $20^{th}$ term of the $A.P.$ $2, -2, -6, -10, \ldots$ is.......

A
$-74$
B
$20$
C
$22$
D
$74$

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Mix Examples - Arithmetic Progressions

An $AP$ consists of $37$ terms. The sum of the three middle most terms is $225$ and the sum of the last three is $429$. Find the $AP$.

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For a finite $A.P.$,the first term is $2$ and the last term is $50$. If the sum of all the terms is $442$,find the common difference $d$.

Medium

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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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The sum of the first $n$ terms of an $A.P.$ is given by $S_{n} = \frac{3n^{2}}{2} + \frac{5n}{2}$. Find the $25^{th}$ term of the $A.P.$

Medium

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Verify that each of the following is an $AP$,and then write its next three terms.
$a, 2a+1, 3a+2, 4a+3, \ldots$

Medium

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The $20^{th}$ term of the $A.P.$ $2, -2, -6, -10, \ldots$ is.......

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An $AP$ consists of $37$ terms. The sum of the three middle most terms is $225$ and the sum of the last three is $429$. Find the $AP$.

For a finite $A.P.$,the first term is $2$ and the last term is $50$. If the sum of all the terms is $442$,find the common difference $d$.

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 $A.P.$

The sum of the first $n$ terms of an $A.P.$ is given by $S_{n} = \frac{3n^{2}}{2} + \frac{5n}{2}$. Find the $25^{th}$ term of the $A.P.$

Verify that each of the following is an $AP$,and then write its next three terms.$a, 2a+1, 3a+2, 4a+3, \ldots$

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Verify that each of the following is an $AP$,and then write its next three terms.
$a, 2a+1, 3a+2, 4a+3, \ldots$