The first term of an arithmetic sequence is 7 and the sixth term is 22. find(a)the common difference; (2)(b)the twelfth term; (2)(c)the sum of the first 100 terms.

d = 3 , a₁₂ = 40 and S = 7775

In an arithmetic sequence the nth term and sum to n terms are

• a = a₁ + (n-1)d• S = [2a + (n-1)d]where d is the common differencea₆ = a₁ + 5d = 22 ⇒ 7 + 5d = 22 ⇒ 5d = 15 ⇔ d = 3a₁₂ = 7 + 11d = 7 +( 11× 3) = 7 + 33 = 40S₁₀₀ = [(2×7) +(99×3)       = 25(14 + 297) = 25(311)= 7775