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