Question

given A.P = 212 ,227,242,257,.........,365.how many terms are there in an A.P​

Answer 1

CORRECT QUESTION :–

• Given A.P = 212 ,227,242,257,.........,362. how many terms are there in an A.P ?

GIVEN :–

• An A.P. series 212 , 227 , 242 , 257 ,......., 362

TO FIND :–

• Total number of terms in A.P. ?

SOLUTION :–

• We know that nth term –

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$\bf \implies \large{ \boxed{ \bf {T_n = a + (n-1)d}}}$

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• Here –

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$\bf \: \: \: {\huge{.}} \: \: \: a = 212$

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$\bf \: \: \: {\huge{.}} \: \: \: d =227 - 212 = 15$

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$\bf \: \: \: {\huge{.}} \: \: \: T_n =362$

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$\bf \: \: \: {\huge{.}} \: \: \:n =total \: \: terms$

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• Now put the value –

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$\bf \implies 362 = 212+ (n-1)(15)$

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$\bf \implies 362- 212 = (n-1)(15)$

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$\bf \implies 150 = (n-1)(15)$

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$\bf \implies (n-1) = \cancel\dfrac{150}{15}$

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$\bf \implies (n-1) = 10$

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$\bf \implies n= 10 + 1$

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$\bf \implies \large{ \boxed{ \bf n= 11}}$

Answer 2

♔ Answer ♔

Given:–

✰ AP = 212, 227, 242, 257,..........,362.

✰ a = 212

✰ d = 227 - 212 = 15

✰ aₙ = 362

Assuming:–

✫ Let the total no. of terms be n.

Formula:–

✫ aₙ = a + (n-1) d

Solution:–

⇢ 362 = 212 + (n-1)15

⇢ 362-212 = 15(n-1)

⇢ 150 = 15(n-1)

⇢ 10 = n-1

⇢ n = 10+1

⇢ n = 11

Total number of terms = 11