Find the 21st term of the ap -4*1/2,-3,-1*1/2
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Answer: The 21st term of the given AP is -12
Step-by-step explanation:
An arithmetic progression (AP) is a sequence of numbers in which each term after the first is obtained by adding a constant value to the previous term. To find the 21st term of the given AP, we need to determine the common difference between consecutive terms and then use it to calculate the 21st term.
The first term of the given AP is -41/2, the second term is -3, and the third term is -11/2. To find the common difference, we can subtract the second term from the first term and the third term from the second term:
-41/2 - (-3) = -1/2
-3 - (-11/2) = -1/2
Since both differences are equal to -1/2, we can conclude that the common difference of the AP is -1/2.
To find the 21st term, we can use the formula for the nth term of an AP:
an = a1 + (n - 1)d
where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
Plugging in the values we know, we get:
a21 = -41/2 + (21 - 1)(-1/2)
a21 = -2 + 20(-1/2)
a21 = -2 - 10
a21 = -12
Therefore, the 21st term of the given AP is -12.
Learn more about Arithmetic Progression:
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Answer:
AP= -4*1/2 , -3 , -1*1/2.........................a21th
Step-by-step explanation:
a = -4*1/2 ,
common difference "d"= [-3 - (- 4*1/2)]
= [-3 + 4*1/2]
= [-6/2 + 9/2]
= 3/2
now,
a21 = a + ( n - 1 )d
= a + (21- 1)d
= a + 20 d
= (-4*1/2) + 20 (3/2)
= [- 9 /2 + 60/2]
= 51/2
= 25*1/2
Therefore, a21 = 25*1/2