Find the 25th Term of the Ap 5 , 4`1/2 , 4,3 1/2 ,3`................. - Mathematics

Find the 25^th term of the AP 5 , 4`1/2 , 4,3 1/2 ,3`.................

The given AP is 5 , 4`1/2 , 4,3 1/2 ,3`.................

First term = 5

Common difference` = 4 1/2 -5 ⇒ 9/2 -5 ⇒(9-10)/2 = -1/2`

∴ a= 5 and d= - `1/2`

Now , `T_25 = a + (25-1) d = a +24 d`

=`5 + 24 xx(-1/2) = 5 -12 =-7`

∴ 25^th term = -7

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Chapter 11: Arithmetic Progression - Exercises 1

Chapter 11 Arithmetic Progression
Exercises 1 | Q 4

Find the 31^st term of an A.P. whose 11^th term is 38 and the 16^th term is 73.

Which term of the A.P. 3, 15, 27, 39, … will be 132 more than its 54^thterm?

Find the indicated terms in the following sequences whose nth terms are:

a_n = (n − 1) (2 − n) (3 + n); a₁, a₂, a₃

Find the next five terms of the following sequences given by:

a₁ = 4, a_n = 4a_n−1 + 3, n > 1.

The 4^th term of an A.P. is three times the first and the 7^th term exceeds twice the third term by 1. Find the first term and the common difference.

The first term of an A.P. is 5 and its 100^th term is -292. Find the 50^th term of this A.P.

Find the number of terms in the A.P.: 18, `15 1/2, 13, ...., -47.`

The 6th term from the end of the AP: 5, 2, -1, -4, …., -31, is ______.

Is 0 a term of the AP: 31, 28, 25, ...? Justify your answer.

Determine the 36^th term of the A.P. whose first two terms are –3 and 4 respectively.