Question

If the nth term of a progression is (4n – 10) show that it is an AP. Find its (i) first term, (ii) common difference (iii) 16 the term.

Answer 1

hope this answer will help you.

Answer 2

i) The first term of AP is -6.

ii) The common difference is 4.

iii) The 16th term is 54.

Step-by-step explanation:

Given : The nth term of a progression is (4n-10).

To find : Show that it is an AP and find its (i) first term, (ii) common difference (iii) 16 the term.

Solution :

The nth term of a progression is $a_n=4n-10$

In order to check whether it an AP or not,

we find some terms by substituting random values of n.

For n = 1

$a_1=4(1)-10\\a_1=-6$

For n =2

$a_2=4(2)-10\\a_2=-2$

For n =3

$a_3=4(3)-10\\a_3=2$

The sequence is  -10,-6,-2,2......

The difference of two consecutive terms should be equal in case of AP.

$-2-(-6)=-2+6=4\\2-(-2)=2+2=4$

We can see the difference is equal.

So, it is an AP.

i) The first term of AP is -6.

ii) The common difference is 4.

iii) The 16th term is

$a_{16}=4(16)-10=64-10=54$

#Learn more

If the nth term of a progression is (4n-10), show that it is an AP. Find is first term?

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