Find the first term of an AP.if 3rd term is 25and 5th term is 39.
Answers
Answer:
Answer is 11
Step-by-step explanation:
We know that for n th term = a + (n-1)d
Case 1: n= 3 for 3rd term
a+. (3-1)d= 25
a+ 2d =25 ---------1
Case 2: n=5 for 5 th term
a+ (5-1)d = 39
a+ 4d = 39 ----------2
a+ 4d = 39
- a+ 2d = 25
___________
2d = 14
d=7
in any of the two equations
a+ (3-1)7 = 25
a+14 =25
a=11
Well, here you can subdivide it in parts of resolution for you to find the first term of this arithmetic sequence. For you understand better it, we will to subdivide it in two parts ... In the first part we will to calculate the common difference and in the second and last part we will to calculate the first term. See the resolution below in the practice.
Common difference.
d = (An - Ak)/(n - k)
d = (39 - 25)/(5 - 3)
d = 14/2
d = 7
The first term.
An = Ak + (n - k) × d
39 = A1 + (5 - 1) × 7
39 = A1 + 4 × 7
39 = A1 + 28
A1 + 28 = 39
A1 = 39 - 28
A1 = 11
Therefore, with all this reasoning that we maked for we to find the first term we can have the conclusion that the same is 11.