Q. 35.0( 5 Votes )

# Find the eleventh

Answer :

We have the AP: 27, 23, 29, …, -65

Here, first term of the series (a) = 27

Common difference of the series (d) = 23 – 27 = -4

Last term of the series (an) = -65

We need to find position of -65, i.e., n.

We know the formula,

an = a + (n – 1)d

-65 = 27 + (n – 1)(-4)

-65 = 27 – 4n + 4

4n = 65 + 27 + 4

4n = 96 = 24

-65 is in the 24th position.

To find the eleventh term from the last term,

Position of the last term = 24th

Position of second last term = (24 – 1)th = 23rd

Position of third last term = (24 – 2)th = 22nd

Similarly, position of eleventh term from the last term = (24 – 10)th = 14th

11th term from the last term = 14th term from the beginning

Thus, taking n = 14, we need to find a14.

The formula of an = a + (n – 1)d

a14 = 27 + (14 – 1)(-4)

a14 = 27 – 52 = -25

Hence, the eleventh term from the last term of the AP is -25.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 