Question

Question 5 In an arithmetic progression, the fifth term is 8, the ninth term is 14 and the last term is 32. Find the sum of all the terms in the progression.​

Answer 1

Answer:

let a is the 1st term of the series and d is the common difference

so,a+(5-1).d=8

=> a+4d=8

again, a+(9-1)=14

=> a+8d=14

subtract ing, we get 4d=6

d=6/4=3/2

a=8-4d=8-4.3/2=8-6=2

so,

2+(n-1).3/2=32

=> (n-1).3/2=32-2=30

=> n-1=30×2/3=20

=> n=20+1=21

so, 32 is the 21 th term

so sum of the all terms

n/2{2a+(n-1).d

21/2{2.2+(21-1).3/2}

=21/2{4+20.3/2}

=21/2{4+30}

=21.34/2

=21.17

=357