The sum of the first five terms of an arithmetic sequence is 85 and its 5th term is 27 a,What is the 4th term? b,What is the 3rd term?
Answers
Answer: (a) 4th term = a4 = 22
(b) 3rd term = a3 = 17
Step-by-step explanation:
Sum of first 5 terms = S5 = 85
a5 = 27
S5 = n/2 ( 2a +(n-1)d) =85
= 5/2 (2a +(5-1)d) = 85
= 5/2 (2a +(4)d) = 85
= 2a + 4d = 85×2/5
= 2a + 4d = 170/5
= 2a + 4d = 34
= 2 ( a + 2d ) = 34 (Since two is a common factor)
= a + 2d = 34/2 = 17
a + 2d = 17 -———(eq : 1)
a5 = a + (n-1)d = 27
= a + (5-1)d =27
= a + 4d = 27
a + 4d = 27———(eq:2)
Now subtract eq:1 from eq:2
a + 4d = 27
- a + 2d = 17
———————-
0 + 2d = 10
2d = 10
d = 10/2 = 5 ———- (eq:3)
substitute eq:3 in eq:1
a + 2(5) =17
a + 10 = 17
a = 17 - 10 = 7
Therefore, a = first term = 7
d = difference = 5
a4 = a + (n-1)d
= 7 + (4-1)5
= 7 + (3)5
= 7 + 15 = 22
a3 = a + (n-1)d
= 7 + (3-1)5
= 7 +(2)5
= 7 + 10 = 17