Question

in an AP if the common difference=-4,find the seventh term (a7)is 4 then find the frist term

Answer 1

It is given in the question that the common difference between the APs is - 4 and the seventh term of the AP is 4 .

Let the first term of the AP be a,


From the properties of the arithmetic progressions, we know

nth term = a + ( n - 1 ) d, where a is the first term, n is the number of terms and d is the common difference.


Comparing the given question with the identity.

= > 7th term = a + ( 7 - 1 )( - 4 )

= > 4 = a + ( 6 x - 4 )

= > 4 = a - 24

= > 4 + 24 = a

= > 28 = a or first term


Therefore,
First term of the given arithmetic progression is 28.
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Answer 2

QUESTION :

in an AP if the common difference=-4,find the seventh term (a7)is 4 then find the frist term

ANSWER :

here it is given that

in an AP

common difference= d = -4

also ,

seventh term = a7 = 4

we have to find that

first term = a = ?

now ,

as we know that

nth term = first term+(no. of terms-1)× common difference

i.e. an= a+(n-1)d

so as

a7 = 4

we can write a7 as

a+(7-1)d = 4

a+6d=4

a= 4-6d

but we know that d=-4

so a=4-6d

=> a=4-6(-4)

=> a=4+24

=> a= 28

NOTE :

while Solving such questions

you must know the formula required to solve the question