Progressions - Model Problems - 1

Chapter: Sequences, Series and Progressions

Arithmetic Progressions

Finding nth term of arithmetic progessions
nth term = a +(n-1)d

Prob: Find the 20th term of the A.P. starting with 4 and common difference 5.

a = 4
d = 5
n = 20

20th term = 4 + (20-1)*5 = 4+19*5 = 4 + 95 = 99.

Finding sum to n terms of AP

Sn = ½ n(a + l)
Sn = ½ n{2a+(n-1)d}


Prob: Find the sum to 20th term of the A.P. starting with 4 and common difference 5.

We found in the earlier problem the 20th term.

a = 4
n = 20
l = 99

Sn = ½ *20(4+99) = 10*103 = 1030.

Insertion of arithmetic means

Prob: Insert 4 arithmetic means between 4 and 19.

We have a = 4, l = 19 and 4 arithmetic means are to be inserted. It means the last term l is the 6th term.

19 = 4+5d
d = 3
the firm A.M. = second term = 4+3 = 7
second A.M. = 7+3 = 10
third A.M. = 10+3 = 13
fourth A.M. = 13+3 = 16