Question

Find the a.p whose third term is 16 and 7th term exceeds the 5th term by 12

Answer 1

Answer:

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Answer 2

Given:-

• Third term of an Ap = 16.
• 7th term exceeds the 5th term by 12.

To find:-

• Find the arithmetic sequence.?

Solutions:-

We have given that;-

Third term of an Ap = 16.

• a3 = 16

=> a + 2d = 16 .......(i).

7th term exceeds the 5th term by 12.

• a7 = a5 + 12

=> a + 6d = a + 4d + 12

=> a - a + 6d - 4d = 12

=> 2d = 12

=> d = 12/2

=> d = 6

Putting the value of d in Eq (i).

=> a + 2d = 16

=> a + 2(6) = 16

=> a + 12 = 16

=> a = 16 - 12

=> a = 4

So, arithmetic sequence is ;-

=> a = 4

=> a + d = 4 + 6 = 10

=> a + 2d = 4 + 2(6) = 4 + 12 = 16

=> a + 3d = 4 + 3(6) = 4 + 18 = 22

Hence, the arithmetic sequence is 4, 10, 16, 22.