2. Find the 20th term of an arithmetic sequence if its 6th term is 14 and 14th term is 6.
2 answers:
Answer:

Step-by-step explanation:
<h3>Arithmetic sequence:</h3>

6th term is 14 ⇒ 
a + (6 - 1)d = 14
a + 5d = 14 --------------(I)
14th term is 6 ⇒
a + (14-1)d = 6
a + 13d = 6 ----------------(II)
Subtract equation (II) from equation(I)
(I) a + 5d = 14
(II) a + 13d = 6
<u>- - -</u>
-8d = 8
d = 8 ÷(-8)

Plugin d = -1 in equation (I)
a + 5(-1) = 14
a -5 = 14
a = 14 + 5
20th term:

= 19 - 19

Answer:
0
Step-by-step explanation:
The number of terms of an Arithmetic progressions has the formular.
Tn = a + ( n - 1 ) d
From the question,
6th term = 14
14th term = 6
Therefore,
a + 5d = 14 -----------(1)
a + 13d = 6 ----------(2)
subtracting
-8d = 8
dividing bothsides by -8

Therefore,
common difference= -1
substituting the value of d into equation (1)
a + 5 ( -1) = 14
a - 5 = 14
a = 14 + 5 = 19
First term = 19
For the 20th term
T 20 = a + 19d
19 + 19 ( -1 )
19-19 = 0
Therefore,
20th term = 0
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