Question

Find the value of the sum 219+226+233+⋯+2018.

Assume that the terms of the sum form an arithmetic series.

Give the exact value as your answer, do not round.

Answer 1

228573

Explanation:

a = 219 (first term)

an = 2018 (last term)

Sn->Sum of n terms

Sn=n/2(a + an) [Where n is no. of terms] -> eq 1

To find number of terms,

an = a + (n-1)d [d->Common Difference] -> eq 2

d= 226-219 = 7

=> d=7

Substituting in eq 2,

2018 = 219 + (n-1)(7)

1799 = (n-1)(7)

1799 = 7n-7

1799 = 7(n-1)

1799/7 = n-1

257 = n-1

n=258

Substituting values in eq 1,

Sn = 258/2(219+2018)

= 129(2237)

= 228573