Question

If the nth term of an a progression is (4n -10) ,show that it is an ap . Find its (i) a (ii) d and (iii) 16 th term

Answer 1

Step-by-step explanation:

for n=1,4n-10=4-10= -6

for n=2,4n-10=8-10= -2

for n=3,4n-10=12-10= 2

so,a = -6

b= -2+-(-6)= -2+6=4

16th term= -6+(16-1).4= -6+60=54

Answer 2

Question :-

If the nth term of an a progression is (4n -10), show that it is an AP. Find its

(i) a

(ii) d

(iii) 16 th term

Solution :-

According to the question,

◘ aₙ of an AP = 4n - 10

From the given conditions,

a₁ = 4(1) - 10

→ a₁ = 4 - 10

→ a₁ = -6

_____________

a₂ = 4(2) - 10

→ a₂ = 8 - 10

→ a₂ = -2

_____________

a₃ = 4(3) - 10

→ a₃ = 12 - 10

→ a₃ = 2

_____________

From above, we get :-

a₂ - a₁ = -2 - (-6) = -2 + 6 = 4

a₃ - a₂ = 2 - (-2) = 2 + 2 = 4

As a₂ - a₁ = a₃ - a₂, so the progression is an arithmetic progression.

________________________

(i) a of the AP is equal to a₁.

→ a = -6

_____________

(ii) d of the AP = a₂ - a₁

→ d = -2 - (-6)

→ d = -2 + 6

→ d = 4

_____________

(iii) 16th term of the AP = a₁₆

→ a₁₆ = a + (16 - 1)d

→ a₁₆ = -6 + 15(4)

→ a₁₆ = -6 + 60

→ a₁₆ = 54