Question

If the number 501 is a term of an A.P. 12,15,18.. Which term will it be?
option (a)165
option (b) 164
option (c) 163
option (d) 162​

Answer 1

GivEn:

• AP = 12, 15,18,...

To find:

• The number 501 is which term of AP.

SoluTion:

Let's 501 be $\sf a_n$ term of AP.

As we know that,

$\star\;\sf a_n = a + (n - 1)d$

Here,

• a = 12

• d = $\sf a_2 - a_1$ = 15 - 12 = 3

• $\sf a_n$ = 501

Therefore,

$:\implies$ 501 = 12 + (n - 1)3

$:\implies$ 501 = 12 + 3n - 3

$:\implies$ 501 = 3n + 9

$:\implies$ 501 - 9 = 3n

$:\implies$ 492 = 3n

$:\implies$ n = $\sf \cancel{ \dfrac{492}{3}}$

$:\implies{\underline{\boxed{\sf{\pink{n = 164}}}}}\;\bigstar$

$\therefore$ Hence, 501 is the $\sf 164^{th}$ term of given AP.

Therefore, Option (b) is correct.

━━━━━━━━━━━━━━━

$\begin{lgathered}\boxed{\begin{minipage}{20 em} \sf \displaystyle \bullet \;\sf n^{th} \;term\;of\;AP\;, a_n = a + (n-1)d \\\\\\ \bullet\;\sf Sum\of\;n\;terms\;of\:an\;AP\;, S_n= \dfrac{n}{2} \left(a + a_n\right) \end{minipage}}\end{lgathered}$

Answer 2

GIVEN :–

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• A.P. → 12 , 15 , 18 , ..............

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TO FIND :–

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• Which term is 501 ?

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SOLUTION :–

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• We know that –

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

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• Here –

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$\bf \: \: \: { \huge{.}} \: \: \: a = 12$

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$\bf \: \: \: { \huge{.}} \: \: \: d =15 - 12 = 3$

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$\bf \: \: \: { \huge{.}} \: \: \: T_n =501$

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$\bf \: \: \: { \huge{.}} \: \: \: n = \: ?$

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• So that –

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$\bf \implies 501 = 12+(n-1)3$

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$\bf \implies 501 - 12= (n-1)3$

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$\bf \implies 489= (n-1)3$

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$\bf \implies (n-1)3 = 489$

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$\bf \implies n - 1= \dfrac{489}{3}$

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$\bf \implies n - 1= 163$

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$\bf \implies n =163 + 1$

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$\bf \implies \large{ \boxed{ \bf n =164}}$

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→ 164th term is 501.

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• Hence , Option (b) is correct.