If the nth term of a progression is (4n – 10) show that it is an AP.

1.	If the nth term of a progression is (4n – 10) show that it is an AP. Find its (i) first term, (ii) common difference (iii) 16 the term.
Answer» T_n = (4_n - 10) [Given] T₁ = (4 x 1 - 10) = -6 T₂= (4 x 2 - 10) = -2 T₃ = (4 x3 - 10) = 2 T₄ = (4 x 4 - 10) = 6 Clearly, [ - 2 -(-6) ] = [ 2 -(-2) ] = [6 - 2] = 4 (Constant) So, the terms -6, -2,2,6,......forms an AP. (i) First term = -6 (ii) Common difference = 4 (iii) T₁₆ = a + (n - 1)d = a + 15d = -6 + 15 x 4 = 54

If the nth term of a progression is (4n – 10) show that it is an AP. Find its (i) first term, (ii) common difference (iii) 16 the term.

Answer»

T_n = (4_n - 10) [Given]

T₁ = (4 x 1 - 10) = -6

T₂= (4 x 2 - 10) = -2

T₃ = (4 x3 - 10) = 2

T₄ = (4 x 4 - 10) = 6

Clearly, [ - 2 -(-6) ] = [ 2 -(-2) ] = [6 - 2] = 4 (Constant)

So, the terms -6, -2,2,6,......forms an AP.

(i) First term = -6

(ii) Common difference = 4

(iii) T₁₆ = a + (n - 1)d = a + 15d = -6 + 15 x 4 = 54