Question

the sum of the 5th and 7th term of an A.P is 52 and 10th term is 46 find the A.P
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Answer 1

Step-by-step explanation:

Given, the sum of the 5th and 7th term of an A.P is 52

=> (a+4d) + (a+6d) = 52

=> 2a + 10d = 52 => a + 5d = 26 -------- (1)

Given, 10th term is 46

=> a + 9d = 46 ----------- (2)

solving (1) & (2)

=> ( a + 9d ) - ( a + 5d )= 46 - 26

=> a + 9d - a - 5d = 20

=> 4d = 20 => d = 20/4 => d = 5

substituting in equal (1)

=> a + 5(5) = 26 => a + 25 = 26

=> a = 26 - 25 => a = 1

.•. required A. P is

1, (1+5), [1+2(5)], [1+3(5)], ..............

ie., 1 , 6 , 11 , 16 , 21 , 26 , 31 , ...............