Question

find the 20th term of the sequence 7,3,-1,-5​

Answer 1

Given,

A sequence 7,3,-1,-5

To Find,

The 20th term of this sequence.

Solution,

In the given sequence,

3-7 = -1-3 = -4

So, from here we can conclude that this sequence is an A.P.

where a = 7 and d = -4

Now

a₂₀ = a+19d

a₂₀ = 7+19(-4)

a₂₀ = 7-76

a₂₀ = -69

Hence, the 20th term of this sequence is -69.

Answer 2

We must recall that:

Arithmetic progression is a progression in which every term after the first is obtained by adding a constant value, called the common difference (d). So, to find the nth term of an arithmetic progression, we know $an=a1+(n-1)d.$

Given series:

$7,3,-1,-5$

first term, $a=7$

difference, $d=3-7=-4$

$n=20$

Use formula, $a_n=a+(n-1)d$

$a_2_0=7+(20-1)(-4)$

$=7+(19)(-4)$

$=7-76$

$=-69$

Hence, $20^t^h$ term is $-69.$