Question

the sum of 5th and 7th terms of an a.p. is 52 and the 10th terms is 46 find the term and the comman difference

Answer 1

Solution:-
Given : Sum of the 5th and 7th term is 52.
∴ a + 4d + a + 6d = 52
2a + 10d = 52 ...............(1)
Also given : 10th term is 46
∴ a + 9d = 46
Multiplying it by 2, we get
2a + 18d = 92 ................(2)
 Now, subtracting equation (1) from equation (2), we get.

  2a + 18d = 92
  2a + 10d = 52
-      -          -
_______________
         8d = 40 
_______________
8d = 40
d = 40/8
d = 5
 Substituting the value of d in equation (1),we get.
2a + 10d = 52
2a + 10*5 + 52
2a = 52 - 50
2a = 2
a = 2/2
a = 1
Therefore, the required AP is 1, 6, 11, 16, 21, 26, 31......
Answer.

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Answer 2

.......................... so terms are 1,6,11,16,21,.........