Question

N th term of the sequence a, a+d ,a+2d,... is :

Answer 1

Answer:

a+(n-1)d

Step-by-step explanation:

∵ 1st term = a+(1-1)d =  a+(0)d

∵ 2nd term = a+(2-1)d = a+(1)d

∵ 3rd term = a+(3-1)d = a+(2)d

∴ nth term = a+(n-1)d

Answer 2

Answer:-

$\red{\bigstar}$ N th term of the sequence $\large\leadsto\boxed{\tt\purple{a+(n-1)d}}$

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• Given:-

• Sequence:- a, a+d, a+2d........... n term.

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• To Find:-

• N th term of the sequence

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• Solution:-

We know,

$\pink{\bigstar}$ $\large\underline{\boxed{\bf\green{a_n = a+(n-1)d}}}$

where,

• a = 1st term

• n = n the term

• d = common difference

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Here,

• First term = a

• 2nd term = a + d

• Common difference = (a+d) - a = d

Therefore, using the Formula:-

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★ 2nd term:-

➪ $\sf a_2 = a + (2-1)d$

➪ $\sf a_2 = a + d$

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★ 3rd term:-

➪ $\sf a_3 = a + (3-1)d$

➪ $\sf a_3 = a + 2d$

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★ 4th term:-

➪ $\sf a_4 = a + (4-1)d$

➪ $\sf a_4 = a + 3d$

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Therefore, clearly the given sequence is in A.P

Hence,

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★ N th term:-

➪ $\large{\bf\pink{a_n = a + (n-1)d}}$

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Therefore, the N th term of the given sequence will be a + (n-1)d.