Question

find the 14th term from the last term of the AP 10,7,4,...,-62.​

Answer 1

Answer:

-23

Step-by-step explanatdata

data

a=10

d=7-10=-3

an= -62

an=a+{n-1}d

-62=10+{n-1}-3

-62=10-3n+3

3n=62+3+10

3n=75

n=75/3

n=25

14th term from last=a+[m-n}d

=10+{25-14} -3

=10+{11}-3

=10-33

=23

Answer 2

Answer: -23

Step-by-step explanation:

Given :

To find the 14th last term of the A.P : 10,7,4,..-62

Solution :

A.P = Arithmetic Progression,.

The series with terms,

$a_1,a_2,a_3,..a_n$

In this type of series, all the terms will have absolutely common difference,.

The common difference = $a_{n} - a_{n-1}$

⇒ $a_2 - a_1$ = 7 - 10 = -3,.

_

The first term of the series ⇒ a = 10,.

The value of 14 th term from the last is given by,

$a_n = l - (n-1)d$

Where,

l is last term of the series,

n , the number of terms from the last,

$a_n$ , the nth  term from the last,

⇒ $a_{n -14} = -62 - (14-1)(-3)$

⇒ $a_{n - 14} = -62 - (13)(-3)$

⇒ $a_{n - 14} = -62 + 39$

⇒ $a_{n - 14} = -62 + 39$

⇒ $a_{n - 14} = -23$

∴ 14th term from the last of the A.P is -23