Question

find the 20th term of an AP whose 7th term is 24 less than the 11th term, first term being 12
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Answer 1

Answer:

126

Step-by-step explanation:

Given ,

First term =a=12

Let the common difference be d

and we know 7th term a7 = a+6d and 11th term a11 = a+10d

According to question ,

a11 − a7 = 24

a+10d−(a+6d) = 24

a+10d−a−6d = 24

4d = 24

d = 6

We know that,

20th term =a20 = a+19d = 12+19(6) = 12+114 = 126

So , the 20th term of AP is 126.

Answer 2

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✤ Required Answer:

⚡GiveN:

• 7th term is 24 less than the 11th term
• First term of the AP = 12

⚡To FinD:

• 20th term of the AP......?

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✤ How to solve?

The above question can be solved by using the nth term finding formula which is given by:

$\large{\cdot{ \boxed{ \rm{a_n = a + (n - 1)d}}}}$

Here,

• an = nth term of the AP
• a = first term of the AP
• n = number of terms of the AP
• d = common difference

☀️ So, Let's solve this question.....

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✤ Solution:

We have,

• 7th term = 11th term - 24
• 1st term = 12

By using nth term formula,

• a7 = a + 6d
• a11 = a + 10d
• a1 = a

According to condition-(1),

➝ a7 = a11 - 24

➝ a + 6d = a + 10d - 24

➝ 10d - 24 = 6d

➝ 4d = 24

➝ d = 24/4 = 6

Finding the 20th term term,

• a20 = a + 19d

Putting the values of a and d,

➝ a20 = 12 + 19(6)

➝ a20 = 12 + 114

➝ a20 = 126

❄ 20th term of the AP = 126

Hence, solved !!

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