Question

the 5th term of an arithmetic sequence is 20 and and the 8th term is 32. a)what is the common difference of the sequence? b)Find it's 11th term?​

Answer 1

GIVEN :-

• 5th term of A.P is 20.
• 8th term of A.P is 32.

TO FIND :-

• 11th term.
• Common difference (d).

TO KNOW :-

$\\ \bigstar \boxed{ \sf \: a_{n} = a + (n - 1)d}$

Here ,

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

SOLUTION :-

♦ 5th term of A.P is 20.

We have ,

• n = 5
• a{5} = 20

Putting values ,

20 = a + (5 - 1)d

20 = a + 4d --------(1)

Also,

♦ 8th term is 32.

We have,

• a{n} = 32
• n = 8

Putting values ,

→ 32 = a + (8-1)d

→ 32 = a + 7d ---------(2)

Subtracting equation (2) by equation (1) ,

→ 20 - 32 = a + 4d - (a + 7d)

→ -12 = a + 4d - a - 7d

→ -12 = -3d

→ d = -12/-3

→ d = 4

Hence , Common difference is 4.

Putting d = 4 in equation (1) ,

→ 20 = a + 4d

→ 20 = a + 4(4)

→ 20 = a + 16

→ a = 20 - 16

→ a = 4

Now , we will find 11th term of A.P.

→ a{11} = a + (11-1)d

Putting values of a and d,

→ a{11} = 4 + 10(4)

→ a{11} = 4 + 40

→ a{11} = 44

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

Answer 2

Answer:

Step-by-step explanation: