the sum of 4th and 8th terms of an ap is 27 and the sum of the 6th and 10th term is 44 find the first three terms of the AP
Answers
Answer:
So the first three terms of the A. P are 23/4,10 & 57/4.
Step-by-step explanation:
Given : -
The 4th term+8th term = 27
The sum of 6th term + 10th term = 44
According to Question-:
T4 + T8 = 27.......equation (i)
T6 + T10 = 44......equstion (ii)
On solving further and subtracting equation (i) from equation (ii),
=> (T6 - T4) + (T10 - T8) = 44 - 27
=> (a + 5d - a - 3d) + (a + 9d - a - 7d) = 17
=> 2a - 2a + 5d + 9d - 3d -7d = 17
On solving we get-:
=> 14d - 10d = 17
=> d = 17/4
Now on putting this value in equation (i) we can get the value of 'a'.
=> T4 + T8 = 27
=> a + 3d + a + 7d = 27
=> 2a + 10d = 27
=> a + 5 x 17/4 = 27
=> a = 27- 85/4
=> 108 - 85/4
=> 23/4 is T1
For T2-:
=> T2= a+d
=> 23/4+17/4
=> 40/4
=> 10
For T3-:
=> T3 = a + 2d
=> 23/4 + 2 x 17/4
=> 57/4
Step-by-step explanation:
Solution is in the attachment
