Question

find the 20th term of the AP whose 7th term is 24 less than 11th term first term being 12​

Answer 1

$\huge\sf\pink{Answer}$

☞ 20th term of the AP is 126

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$\huge\sf\blue{Given}$

✭ 7th term of an AP is 24 less than its 11th term

✭ First term (a) = 12

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$\huge\sf\gray{To \:Find}$

◈ The 20th term of the AP?

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$\huge\sf\purple{Steps}$

We know that the $\sf n^{th}$ term of an AP is given by,

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

So as per the question,

➝ $\sf a_7 = a+(7-1)d$

➝ $\sf a_7 = a+6d \:\:\: -eq(1)$

Similarly,

➝ $\sf a_{11} = a+(11-1)d$

➝ $\sf a_{11} = a+10d \:\:\: -eq(2)$

☯ $\underline{\sf As \ Per \ the \ Question}$

➳ $\sf a_{11}-a_{7} = 24$

➳ $\sf a+10d-(a+6d) = 24$

➳ $\sf a+10d-a-6d=24$

➳ $\sf 4d=24$

➳ $\sf d=\dfrac{24}{4}$

➳ $\sf \red{d=6}$

Now that we know the value of a & d we shall find the value of the 20th term

»» $\sf a_n=a+(n-1)d$

»» $\sf a_{20} = 12+(20-1)(6)$

»» $\sf a_{20} = 12+(19)(6)$

»» $\sf a_{20} = 12+114$

»» $\sf \orange{a_{20} = 126}$

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Answer 2

Answer:

20th term of the AP is 126

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\huge\sf\blue{Given}Given

✭ 7th term of an AP is 24 less than its 11th term

✭ First term (a) = 12

━━━━━━━━━━━━━

\huge\sf\gray{To \:Find}ToFind

◈ The 20th term of the AP?

━━━━━━━━━━━━━

\huge\sf\purple{Steps}Steps

We know that the \sf n^{th}n

th

term of an AP is given by,

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

a

n

=a+(n−1)d

So as per the question,

➝ \sf a_7 = a+(7-1)da

7

=a+(7−1)d

➝ \sf a_7 = a+6d \:\:\: -eq(1)a

7

=a+6d−eq(1)

Similarly,

➝ \sf a_{11} = a+(11-1)da

11

=a+(11−1)d

➝ \sf a_{11} = a+10d \:\:\: -eq(2)a

11

=a+10d−eq(2)

☯ \underline{\sf As \ Per \ the \ Question}

As Per the Question

➳ \sf a_{11}-a_{7} = 24a

11

−a

7

=24

➳ \sf a+10d-(a+6d) = 24a+10d−(a+6d)=24

➳ \sf a+10d-a-6d=24a+10d−a−6d=24

➳ \sf 4d=244d=24

➳ \sf d=\dfrac{24}{4}d=

4

24

➳ \sf \red{d=6}d=6

Now that we know the value of a & d we shall find the value of the 20th term

»» \sf a_n=a+(n-1)da

n

=a+(n−1)d

»» \sf a_{20} = 12+(20-1)(6)a

20

=12+(20−1)(6)

»» \sf a_{20} = 12+(19)(6)a

20

=12+(19)(6)

»» \sf a_{20} = 12+114a

20

=12+114

»» \sf \orange{a_{20} = 126}a

20

=126

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✌HOPE YOU GET YOUR ANSWER.