Question

form an AP by inserting 5 terms between 11 and -7​

Answer 1

Here we have to form an AP between the numbers 11 and -7.

Let,

• Five terms  = a₁, a₂, a₃, a₄, a₅

• Common difference = d

• First term (a) = -7

• Last term (b) = 11

• Number of terms (n) = 5

⇒ AP =  -7, a₁, a₂, a₃, a₄, a₅, 11

Common difference can be calculated by the equation:

$\boxed{\bold{\sf{d=\dfrac{b-a}{n+1}}}}$

Applying the values to the equation:

$\implies\sf{d=\dfrac{11-(-7)}{5+1}}$

$\implies\sf{d=\dfrac{18}{6}}$

$\implies\sf{d=3}$

Therefore the terms are:

• a₁ = -7 + 3 = -4

• a₂ = -4 + 3 = -1

• a₃ = -1 + 3 = 2

• a₄ = 2 + 3 = 5

• a₅ = 5 + 3 = 8

$\boxed{\bold{\sf{\therefore AP=-7,-4,-1,2,5,8,11}}}$