Question

The 11^th term of the AP: ${\displaystyle -5,\frac{-5}{2},0,\frac{5}{2},...}$ is ______.

विकल्प

• –20

• 20

• –30

• 30

Answer 1

The 11^th term of the AP: ${\displaystyle -5,\frac{-5}{2},0,\frac{5}{2},...}$ is 20.

Explanation:

First term, a = – 5

Common difference,

d = ${\displaystyle 5-\left(\frac{-5}{2}\right)}$

= ${\displaystyle -\frac{5}{2}+5}$

= ${\displaystyle \frac{-5+10}{2}}$

= ${\displaystyle \frac{5}{2}}$

n = 11

We know that the n^th term of an AP is

a_n = a + (n – 1)d

Where,

a = first term

a_n is n^th term

d is the common difference

a₁₁ = ${\displaystyle -5+(11-1)\left(\frac{5}{2}\right)}$

a₁₁ = ${\displaystyle -5+\left(10\right)\left(\frac{5}{2}\right)}$

a₁₁ = – 5 + 5(5)

a₁₁ = – 5 + 25

a₁₁ = 20