Question

The 5th term of an arithmetic sequence is 20 and the 8th term is 32 . (a) What is the common difference of this sequence? (b) Find its 11th term
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Answer 1

Answer:

Hence , 11th term of the A.P is 44.

Step-by-step explanation:

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Answer 2

Answer :

• The 11th term of the AP is 44.

Given :

• The 5th term of an arithmetic sequence is 20 and the 8th term is 32.

To Find :

• The 11th term & common difference (d) ?

Solution :

• Let the 11th term be x.

Using formula,

• a_{n} = a + (n - 1)d

Here,

• a{n} > 'n'th term.
• a > 1st term.
• n > Number of terms.
• d > Common difference.

So,

• n = 5
• a{5} = 20

Putting values,

➛ 20 = a + (5 - 1)d

➛ 20 = a + 4d Eⁿ (1)

Also,

• 8th term is 32.

We have,

• a{n} = 32
• n = 8

Putting values,

➛ 32 = a + (8 - 1)d

➛ 32 = a + 7d Eⁿ (2)

Substracting, equation (1) & equation 2

➛ 20 - 32 = a + 4d - (a + 7d)

➛ 12 = a + 4d - a - 7d

➛ -12 = -3d

➛ d = -12/3

➛ d = 4

Therefore,

• Common difference (d) is 4.

Putting, d = 4 in equation 1,

➛ 20 = a + 4d

➛ 20 = a + (4)4

➛ 20 = a + 16

➛ a = 20 - 16

➛ a = 4

Now, find 11th term of AP

• a{11} = a + (11 - 1)d

We get substituting the given values a & d

➛ a{11} = 4 + 10(4)

➛ a{11} = 4 + 40

➛ a{11} = 44

Hence,

• The 11th term of the AP is 44.