Question

In an arithmetic sequence 10th term is 20 and 20th term is 10.what is the common difference? write the first term? what is the algebraic expression for this sequence?​

Answer 1

Answer:

first term = 29

common difference= -1

Answer 2

Given:-

• 10 th term of an arithmetic sequence = 20

• 20 th term of an arithmetic sequence = 10

To Find:-

• Common Difference

• First Term

Formula Used:-

• ${\boxed{\bf{a_n = a+(n-1)d}}}$

Solution:-

Firstly,

$\sf :\implies\:a_{10} = 20$

$\sf :\implies\:a+(10-1)d=20$

$\sf :\implies\:a+9d = 20$

$\sf :\implies\:a= 20-9d$ ___ {1}

Now,

$\sf :\implies\:a_{20} = 10$

$\sf :\implies\:a+(20-1)d=10$

$\sf :\implies\:a+19d = 10$

Putting value of a,

$\sf :\implies\:20-9d+19d = 10$

$\sf :\implies\:20+10d = 10$

$\sf :\implies\:10d = 10-20$

$\sf :\implies\:d = \dfrac{-10}{10}$

$\sf :\implies\:d = -1$

Putting value of d in {1},

$\sf :\implies\:a= 20-9(-1)$

$\sf :\implies\:a= 20+9$

$\sf :\implies\:a= 29$

Hence, The Common Difference and First term of an A.P. are -1 and 29 respectively.

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