Question

-
The 7th term of an AP is -4 and its 13th term is -16. Find the AP
​

Answer 1

find the ap by putting values as

a, a+d , a+2d............,a+nd

Answer 2

Question -

The 7th term of an AP is - 4 and its 13th term is - 16. Find the AP

Solution -

Given,

$t_{7} = - 4$

$t_{13} = - 16$

Let,

The first term be a and the common difference be d.

Now,

We know that,

nth term = a+(n-1)d

$t_{7} \implies a + (7 - 1)d = - 4$

$t_{7} \implies \: a \: + 6d = - 4</p><p>$

$t_{7} \implies \: a = - 4 - 6d......1)$

And,

$t_{13}\implies a + (13 - 1)d = - 16$

$t_{13}\implies a + 12d = - 16$

$t_{13}\implies - 4 - 6d + 12d = - 16(by \: 1)$

$t_{13}\implies - 4 + 6d = - 16$

$t_{13}\implies 6d = - 16 + 4$

$t_{13}\implies 6d = - 12$

$t_{13}\implies d = - 6$

By putting the value of d in equation 1 we will get -

$a = - 4 - 6( - 2)$

$a = - 4 + 12$

$a = 8$

Therefore the AP is 8,6,4,2,0,-2,-4.......