Question

In an A.P. the 10th term is 46, sum of 5th and 7th term is 52. Find the A.P.

Answer 1

In an A. P, there is a first term (a) and a common difference (d) ........
first term =a
second term=a+d
third term =a+2d
.......and so on
10th term=a+9d=46
5th term=a+4d
7th term=a+6d
sum of fifth and seventh term=52
a+4d+a+6d=52
2a+10d=52
2(a+5d)=52
2a+10d-(a+9d) =a+d=52-46=6
a+9d-(a+d)=46-6=40
8d=40
d=5
a=1

Then the A. P = 1,6,11,16.......

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Answer 2

10th Term in Ap
a
$a + 9d = 46$
Sum of 5th term and 7th term
$a + 4d + a + 6d = 52$
i.e
$2a + 10d = 52$
multiplying equations 1 by 2 we get,
$2a + 18d = 92$
subtracting equation 3 from equation 4
$2a + 18d = 92 \\ - 2a + 10d = 52 \\ 8d = 40$
$d = \frac{40}{8} \\ d = 5$
put d=5 in equation 1 we get.
$a + 9(5) = 46 \\ a + 45 = 46 \\ a = 46 - 45 \\ a = 1$
first term =a = 1 and common difference d= 5