Question

in an ap the first term is a and the 20th term is b. the sum of the 10th and 11th term is

Answer 1

Answer:

The sum of the 10th and 11th term is (a + b).

Step-by-step explanation:

We are given,

a1 = a

a(20th) = b

We know that,

a(nth) = a + (n - 1)d

a(20th) = a + (20 - 1)d

b = a + 19d

Now,

a + b = a + a + 19d

a + b = 2a + 19d ----- 1

Now, we are asked to find the sum of 10th and 11th term,

a(10th) = a + (10 - 1)d

a(10th) = a + 9d

Similarly,

a(11th) = a + (11 - 1)d

a(11th) = a + 10d

Thus,

a(10th) + a(11th) = a + 9d + a + 10d

= 2a + 19d

But from eq.1 we get,

a + b = 2a + 19d

Thus,

a(10th) + a(11th) = a + b

OR

a(10th) + a(11th) = a(1st) + a(20th)

Hence, the sum of the 10th and 11th term is (a + b).

Hope it helped and you understood it........All the best