Given a and d for the following A.P., find the following A.P.:

a = 100, d = –7

Formula Used.

a_n = a + (n–1)d

If a = 100, d = –7

Then a₁ = a + (n–1)d = 100 + (1–1)(–7) = 100

a₂ = a + (n–1)d = 100 + (2–1)(–7) = 100 + (–7)×1 = 93

a₃ = a + (n–1)d = 100 + (3–1)(–7) = 100 + (–7)×2 = 86

a₄ = a + (n–1)d = 100 + (4–1)(–7) = 100 + (–7)×3 = 79

a_n = a + (n–1)d = 100 + (n–1)(–7) = 107 – 7n

∴ The A.P is 100, 93, 86, 79……107–7n