Question

20th term of the progression 10,7,4,..... will be​

Answer 1

*I have assumed that it's Arithmetic Progression *

Answer:

$\underline{\boxed{\mathsf{20th\: term \: = (-47) }}}$

Step-by-step explanation:

$\large \underline{\underline{\textbf{Given...}}}$

$\textsf{A.P : 10,7,4.........n}$

We need to find 20th term

$\large \underline{\underline{\textbf{Solution...}}}$

Here we have

AP : 10,7,4........n

Thus

$\mathsf{a_1 =\: First\: term\: =\:10}$

$\mathsf{a_2 =\: Second\: term\: =\:7}$

$\mathsf{a_n =\:20th\: term\: = {a}_{20} }$

Now by formula

$\boxed{\bigstar \: \: \mathsf{a_n\: = \: a_1 + (n-1)d \:\: \bigstar }}$

Where

$\mathsf{a_n =\:20th\: term\: = {a}_{20} }$

$\mathsf{a_1 =\: First\: term\: =\:10}$

$\textsf{n = number of terms = 20 }$

Now

$\mathsf{d\: =\: Common \: difference \: =\: a_2 - a_1 }$

$\implies \mathsf{d \: = \:7-10 = -3}$

Now putting all values in the above formula we have

$\mathsf{{a}_{20}\: = \: 10 + (20-1)-3}$

$\implies \mathsf{{a}_{20}\: = \: 10 + (19)-3}$

$\implies \mathsf{{a}_{20}\: = \: 10-57}$

$\implies \mathsf{{a}_{20}\: = \: -47}$

$\underline{\textbf{Therefore required answer is}}$

$\underline{\boxed{{a}_{20}\: = \: -47}}$

Answer 2

Answer: 20th term will be -47

EXPLANATION:

Given,

AP: 10, 7, 4,........

The first term of AP = a = 10

Common Difference = d = 7 - 10 = -3

20th term:

=> a + 19d

=> (10) + 19(-3)

=> 10 + (-57)

=> 10 - 57

=> -47

Therefore, 29th term of AP is -47.