# If 5th and 6th Terms of an A.P Are Respectively 6 and 5. Find the 11th Term of the A.P - Mathematics

Sum

If 5th and 6th terms of an A.P are respectively 6 and 5. Find the 11th term of the A.P

#### Solution

The general term of an A.P is given by

t_n = a + (n - 1)d

Now t_5 = 6

=> a + (5 - 1)d = 6

=> a + 4d = 6 ....(i)

And t_6 = 5

=> a + (6 - 1)d = 5

=> a + 5d = 5 ...(ii)

Substracting (ii) from (i) we get

-d = 1

=> d = -1

Substituting d = -1 in (i) we get

a + 4(-1) = 6

=> a - 4 = 6

=> a = 10

=> t_n = 10 + (n - 1)(-1)

=> t_11 = 10 + (11 - 1)(-1) = 10 - 10 = 0

Concept: Arithmetic Progression - Finding Sum of Their First ‘N’ Terms.
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#### APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 10 Arithmetic Progression
Exercise 10 (A) | Q 12 | Page 138