Question

Question 8 An A.P. consists of 50 terms of which 3 rd term is 12 and the last term is 106. Find the 29 th term

Class 10 - Math - Arithmetic Progressions Page 106

Answer 1

hopes I helped ................

Answer 2

General term or nth term of A.P
The general term or nth term of A.P is given by an = a + (n – 1)d, where a is the first term, d is the common difference and n is the number of term.----------------------------------------------------------------------------------------------------
Solution:

Given :

a3 = 12
a50 = 106

We know that,
an = a + (n − 1) d

a3 = a + (3 − 1) d
12 = a + 2d … (i)

Similarly, a50 = a + (50 − 1) d
106 = a + 49d … (ii)

On subtracting (i) from (ii), we get
94 = 47d
d = 2

From equation (i), we get
12 = a + 2 (2)
a = 12 − 4 = 8

a29 = a + (29 − 1) d
a29 = 8 + (28)2
a29 = 8 + 56 = 64

Hence , 29th term is 64.

----------------------------------------------------------------------------------------------------

Hope this will help you...