Question

Which term of the AP 21,42,63,84...is210?

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Term=10th}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies A.P= 21,42,63,84,.. \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Which \: term \: is \: 210 =?$

• According to given question :

$\tt \circ \:First \: term ( a_{1} )= 21 \\ \\ \tt \circ \: Common \: difference(d) = 21 \\ \\ \tt \circ \: Last \: term ( a_{n} )= 210 \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies a_{n} = a + (n - 1)d \\ \\ \tt: \implies 210 = 21 + (n - 1) \times 21 \\ \\ \tt: \implies 210 = 21 + (n - 1) \times 21 \\ \\ \tt: \implies 210 - 21= (n - 1) \times 21 \\ \\ \tt: \implies 189 = (n - 1) \times 21 \\ \\ \tt: \implies \frac{189}{21} =n - 1 \\ \\ \tt: \implies 9 + 1 = n \\ \\ \green{\tt: \implies n = 10} \\ \\ \green{\tt \therefore 210 \: is \: 10th \: term \: of \: this \: A.P}$

Answer 2

Aɴꜱᴡᴇʀ

☞ 210 is the 10th term of the given A.P

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Gɪᴠᴇɴ

➜ A.P ➳ 21,42,63,84................

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Tᴏ ꜰɪɴᴅ

➤ Which term of the A.P is 210?

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Sᴛᴇᴘꜱ

❍ First let's find the value of a (first term) and d (common difference)

$\dashrightarrow{} \sf{}a = 21 \\ \\ \dashrightarrow{} \sf{}d = 42 - 21 = 21$

So we know that,

$\underline {\boxed{ \sf\red{a_n = a+(n-1) d }}}$

So substituting the values,

$\leadsto{} \sf{}a_n = a+(n-1) d \\ \\ \leadsto \sf{}210 = 21 + (n - 1)21 \\ \\ \leadsto \sf{}210 - 21 = (n - 1)21 \\ \\ \leadsto{} \sf{}189 = (n - 1)21 \\ \\ \leadsto \sf \cancel \frac{189}{21} = (n - 1) \\ \\ \leadsto \sf{}9 + 1 = n \\ \\ \pink{ \leadsto{} \sf{}n = 10}$

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