Question

The 26 th 11 th and the last term of an AP are 0 3 and -1/5 respitvely so find the d and number of terms

Answer 1

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Answer 2

Solution:-

Given:-

a26 = 0,

a11 = 3

an = -1/5

To Find:-

Common Difference (d) = ?

Find:-

=) a26 = 0

=) a + 25d = 0

=) a = - 25d ___________(1)

Now,

a11 = 3

=) a + 10d = 3

=) -25d + 10d = 3

=) -15d = 3

=) d = -3/15

=) d = -1/5

Substituting [ d = -1/5 ] in eq (1). we get,

=) a = -25 ( -1/5)

=) a = 5

Now,

an = a + ( n - 1)d

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

=) -1/5 - 5 = ( n - 1)(-1/5)

=) ( -1 - 25)/5 = ( n -1)(-1/5)

=) -26/5 = (n-1)( -1/5)

=) -26 = -( n-1)

=) 26 = n -1

=) n = 27.