(A) Given: $a = -1$ and $d = \frac{1}{2}$.The general form of an $AP$ is $a_1, a_2, a_3, a_4, \dots$ where $a_n = a + (n-1)d$.$a_1 = a = -1$$a_2 = a +

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(A) Given: $a = -1$ and $d = \frac{1}{2}$.The general form of an $AP$ is $a_1, a_2, a_3, a_4, \dots$ where $a_n = a + (n-1)d$.$a_1 = a = -1$$a_2 = a + d = -1 + \frac{1}{2} = -\frac{1}{2}$$a_3 = a + 2d = -1 + 2(\frac{1}{2}) = -1 + 1 = 0$$a_4 = a + 3d = -1 + 3(\frac{1}{2}) = -1 + \frac{3}{2} = \frac{1}{2}$Thus,the first four terms of the $AP$ are $-1, -\frac{1}{2}, 0, \frac{1}{2}$.

Class 10 Mathematics Arithmetic Progressions Textbook -Arithmetic Progressions

Difficult

Write the first four terms of the $AP,$ when the first term $a$ and the common difference $d$ are given as follows: $a = -1, d = \frac{1}{2}$

A
-$1$,-$1$/$2$,$0$,$1$/$2$
B
-$1$,-$1$/$2$,$1$/$2$,$1$
C
-$1$,$0$,$1$/$2$,$1$
D
-$1$,-$1$/$2$,$0$,$1$

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Arithmetic Progressions

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Textbook -Arithmetic Progressions

Find the sum of the first $40$ positive integers divisible by $6$.

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In an $AP$,given $a_{3} = 15$ and $S_{10} = 125$,find $d$ and $a_{10}$.

Medium

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If the $3^{rd}$ and the $9^{th}$ terms of an $AP$ are $4$ and $-8$ respectively,which term of this $AP$ is zero?

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Determine the $AP$ whose third term is $16$ and the $7^{th}$ term exceeds the $5^{th}$ term by $12$.

Medium

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Ramkali saved ₹ $5$ in the first week of a year and then increased her weekly savings by ₹ $1.75$. If in the $n$-th week,her weekly savings become ₹ $20.75$,find $n$.

Medium

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Write the first four terms of the $AP,$ when the first term $a$ and the common difference $d$ are given as follows: $a = -1, d = \frac{1}{2}$

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Find the sum of the first $40$ positive integers divisible by $6$.

In an $AP$,given $a_{3} = 15$ and $S_{10} = 125$,find $d$ and $a_{10}$.

If the $3^{rd}$ and the $9^{th}$ terms of an $AP$ are $4$ and $-8$ respectively,which term of this $AP$ is zero?

Determine the $AP$ whose third term is $16$ and the $7^{th}$ term exceeds the $5^{th}$ term by $12$.

Ramkali saved ₹ $5$ in the first week of a year and then increased her weekly savings by ₹ $1.75$. If in the $n$-th week,her weekly savings become ₹ $20.75$,find $n$.

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