Question

The 10TH term from the end of an A.P is its 11th term from beginning and its value is 55.If its first term is 5,find the common difference,the number of terms and the last terms

Answer 1

In this AP

a=5

10th term=a+9d

a+10d=55

as a=5 (given)

therefore,

5+10d=55

10d=50

d=5

Now,

total no of terms=(10+11)-1

=20

we are subtracting 1 so, that the 10th term won't get counted twice

now,

20th term=a+19d

=5+(19*5)

=5+95

=100

Answer 2

The common difference is 5, the number of terms is 20, and the last term is 100.

Given,

The 10 th term from the end of A.P = 11th term from the beginning = 55

The First-term of A.P = 5

To Find,

The common difference, number of terms, and the last term of the A.P.

Solution,

In the given A.P

a=5,

Also,

a₁₁ = 55

a+10d=55

5+10d=55

10d=50

d=5

Now,

total no of terms= (10+11)-1 =20

we are subtracting 1 so, that the 10th term won't get counted twice

Now,

The last term will be the 20th term, So

a₂₀ = a+19d

a₂₀ = 5+(19*5)

a₂₀ = 5+95

a₂₀ = 100

Hence, the common difference is 5, the number of terms is 20, and the last term is 100.