Question

An arithmetic series has its 5th term equal to 22 and its 15th term equal to 62. Find its 100th term.

Answer 1

Answer:

100th term = 402

Step-by-step explanation:

5th term=22

An=22, n=5

An=a+(n-1)d

A5=a+(5-1)d

22=a+4d--eq1

15th term=62

An=62, n=15

An=a+(n-1)d

A15=a+(15-1)d

62=a+14d--eq2

Add eq1 and eq2, we get

10d=40

d=40/10

d=4

Substituting d=4 in eq1

a+4d=22

a+4(4)=22

a+16=22

a=22-16

a=6

100th term

n=100, a=6, d=4

An=a+(n-1)d

A100=6+(100-1)4

A100=6+(99)4

A100=6+396

A100=402

Therefore, the 100th term is 402.