Question

Find the middle term of the A.P. 3, 8, 13,......, 253

Answer 1

Step-by-step explanation:

ATQ. the last number in the series is 253

Therefore Tn= 253

formula of Tn = a + (n-1) d

Here a= 3 (first term)

d= 5 (common difference between the numbers)

putting the values we get

Tn = 3 + (n-1) 5 = 253

=》 3 + 5n - 5 = 253

=》 5n- 2= 253

=》5n= 253+2

=》 n= 255/5

=》 n= 51

Therefore number of terms in this series is 51

So middle term will be 26th term

now a26 = a + (n-1) d

= 3 + (26-1) 5

= 3+ 25× 5

= 3+ 125

= 128

Therefore middle term will be 128

Answer 2

Solution :

• First term = 3

• Common difference = 5

• Last term = 253

⇒ An = a + ( n - 1 ) d

→ 3 + (n-1) 5 = 253

→ 3 + 5n - 5 = 253

→ 5n- 2= 253

→ 5n= 253+2

→ n= 255/5

→ n= 51

There are 51 terms in this series

So middle term will be 26th term

A26 = a + 25d

→ 3+ 25× 5

→ 3+ 125

→ 128

Therefore middle term will be 128