The arithmetic sequence a1 is defined by the formula:

a1 = 4

a1=ai-1 + 11

Find the sum of the first 650 terms in the sequence.

2,322,775

Step-by-step explanation:

Given a1 = 4 and ai = ai-1 + 11

when i = 2

a2 = a2-1+11

a2 = a1+11

a2 = 4+11

a2 = 15

when i = 3

a3 = a2+11

a3 = 15+11

a3 = 26

The sequence formed by a1, a2, a3 ... is am arithmetic sequence as shown;

4, 15, 26 ...

Sum of nth term of an arithmetic sequence = n/2{2a + (n-1) d}

a is the first term = 4

d is the common difference = 15-4 = 26-15 = 11

n is the number of terms.

Since we are to find the sum of the first 650 terms in the sequence, n = 650

S650 = 650/2{2 (4) + (650-1) 11}

S650 = 325{8 + (649) 11}

S650 = 325 (8+7,139)

S650 = 325*7147

S650 = 2,322,775