Question

The 26th, 11th and the last term of an A.P. are 0,3 and -1/5 respectively. Find the common difference and the number of terms.

Answer 1

Given :

• a₂₆ = 0
• a₁₁ = 3
• aₙ = -1/5

To Find :

• Common difference and Number of terms

Solution :

As we know that, aₙ = a + (n - 1)d

First of all we will make three equations :

0 = a + (26 - 1)d

⇒0 = a + 25d ...(1)

3 = a + (11 - 1)d

⇒3 = a + 10d ...(2)

Similarly,

-1/5 = a + (n - 1)d

⇒ -1/5 = a + (n - 1)d ..(3)

$\rule{200}{2}$

Took equation (1) and (2)

⇒0 = a + 25d

⇒3 = a + 10d

_____________________

0-3 = a-a + 25d - 10d

_____________________

⇒-3 = 0 + 15d

⇒15d = -3

⇒d = -3/15

⇒d = -1/5

$\therefore$ Common Difference is -1/5

And,

⇒0 = a + 25(-1/5)

⇒a - 5 = 0

⇒a = 5

$\therefore$ First term is 5

__________________________________

Put value of a and d in (3)

⇒-1/5 = a + (n - 1)(-1/5)

⇒-1/5 = 5 + (n - 1)(-1/5)

⇒-1/5 - 5 = (n - 1)(-1/5)

⇒ -5.2 = (n - 1) (-1/5)

⇒n - 1 = -5.2 * ( - 5/1)

⇒n - 1 = 26

⇒n = 26 + 1

⇒n = 27

$\therefore$ Number of terms is 27