The AP is, 1 , 6, 11, 16, 21, 26, 31,
Step-by-step explanation:
From the question;
Sum of fifth term and 7th term is 52 That is; 5th term + 7th term = 5210th term is 46
We are required to find the AP;
We need to know that in an AP ;
nth term = a + (n-1) d , where a is the first term and d is the common difference
Therefore, In this case;
5th term = a + 4d
7th term = a + 6d
Therefore;
5th term + 7th term = 2a + 10d = 52 eqn 1
10th term = a + 9d
Thus, a + 9d = 46 eqn 2We can solve eqn 1 and eqn 2 simultaneously to get the value of a and d
2a + 10d = 52
a + 9d = 46
Multiplying the second equation by 2, we get;
2a + 10d = 52
2a + 18d = 92
Eliminating a by subtracting the two equations; we get;
-8d = -40
d = 5
Solving for a
a + 9d = 46
a = 46 - 9d
= 46 - 9(5)
= 46 - 45
a = 1
Thus, the first term, a= 1 and the common difference, d= 5
Therefore;
First term = a = 1
Second term = a + d = 1 + 5 = 6
Third term = a + 2d = 1 + 2(5) = 11
Fourth term = a + 3d = 1 + 3(5) =16
Fifth term = a + 4d = 1 + 4(5) = 21
Sixth term = 1 + 5d = 1 + 5(5) = 26
Seventh term = 1 + 6d = 1 + 6(5) = 31
Thus,
The AP is, 1 , 6, 11, 16, 21, 26, 31,