Question

find the 21st term of an AP = - 9/2,-3,-3/2​

Answer 1

The 21st term is 51/2

Solution:

Given that,

The arithmetic sequence is:

$\frac{-9}{2}, -3, \frac{-3}{2}$

Find the common difference between a term and its previous term

$d = -3-(\frac{-9}{2})\\\\d = -3+\frac{9}{2}\\\\d = \frac{-6+9}{2}\\\\d = \frac{3}{2}$

The nth term in an AP is given as:

$a_n = a_1 + (n-1)d$

Where,

n is the nth term

d is the common difference

$a_1$ is the first term

Find the 21st term:

Substitute

$n = 21\\\\d = \frac{3}{2}\\\\a_1 = \frac{-9}{2}$

Therefore,

$a_{21} = \frac{-9}{2} + (21-1) \times \frac{3}{2}\\\\a_{21} = \frac{-9}{2} + 20 \times \frac{3}{2}\\\\\a_{21} = \frac{-9}{2} + 30\\\\a_{21} = \frac{-9+60}{2}\\\\a_{21} = \frac{51}{2}$

Thus 21st term is found

Learn more about AP

Sum of three consecutive terms of an Arithmetic Progression is 42 and their product is 2520.  Find the terms of the Arithmetic Progression.

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Which term of the Arithmetic Progression - 7,-12,-17,-22 will be -82 ? Is -100 any term of the A.P. ? Give reason for your answer.

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Answer 2

Answer:

a= -9/2

d=3/2

n=21

d= b-a

b=-3-(-9/2)

=3/2

an =a+(n-1)d

put the givens in this equation

will be

an= -9/2+(21-1)3/2

an=-9/2+(20)3/2

an= -9/2+60/2

an= 51/2

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