Question

the 6th term of an AP is -10 and 10th term is -26.Detwrmine the 15th term of an AP

Answer 1

Hey!!

a6 = a + 5d
-10 = a + 5d

a10 = a + 9d
-26 = a + 9d

solving 1st and 2nd equations

a+ 5d= -10
a+ 9d = -26
----------------
-4d = 16.
d = -4

a = -10 - 5× -4
a = -10 +20
a = 10

a15 = a + 14d
a15 = 10 + 14×-4
a15 = 10 - 56
a15 = -46
✌✌Hope it helps u

❤All the best for ur exam

Answer 2

HEY, HERE'S THE ANSWER⏬

Given ,
$a_{6} = - 10 \\ = > a_{6} = a + 5d = - 10 - - - - i\\ and \: ... a_{10} = - 26 \\ = > a + 9d = - 26 - - - - ii$
From eq. (i) and (ii) we get :
$a + 9d = - 26 \\ a + 5d = - 10 \\ - \: \: \: - \: \: \: \: \: \: \: \: \: + \\ \: \: \: \: 4d = - 16 \\ \: \: = > d = - 4$

Putting the value of "d" in eq. (i) :

a + 5d = -10
=> a + 5(-4) = -10
=> a = -10 + 20
=> a = 10 .

Now , The 15th term = a + (15-1) d
= 10 + 14 × (-4)
= 10 - 56
= - 46

HOPE IT HELPS YOU ✌️!!!