Question

find the sum of the sequence 51,54,57....249​

Answer 1

Hello !!

Find common difference.

d = (An - Ak)/(n - k)

d = (54 - 51)/(2 - 1)

d = 3/1

d = 3

Find the position of the term 249.

An = A1 + (n - 1) × d

249 = 51 + (n - 1) × 3

249 = 51 + 3n - 3

249 = 3n + 51 - 3

249 = 3n + 48

3n + 48 = 249

3n = 249 - 48

3n = 201

n = 201/3

n = 67

Find the sum of the first term 67 first terms.

Sn = (A1 + An) × (n/2)

S67 = (51 + 249) × (67/2)

S67 = 300 × 33.5

S67 = 10050

Final result : 10050 is the sum.

I hope I have collaborated !