Question

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.

Answer 1

d = 3 , a₁₂ = 40 and S$x_{100}$ = 7775

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

• a$n$ = a₁ + (n-1)d

• S$_n$ = $\frac{n}{2}$[2a + (n-1)d]

where d is the common difference

a₆ = a₁ + 5d = 22 ⇒ 7 + 5d = 22 ⇒ 5d = 15 ⇔ d = 3

a₁₂ = 7 + 11d = 7 +( 11× 3) = 7 + 33 = 40

S₁₀₀ = $\frac{50}{2}$[(2×7) +(99×3)

      = 25(14 + 297) = 25(311)= 7775