The arithmetic sequence a_ia

i



a, start subscript, i, end subscript is defined by the formula:

a_1 = 5a

1



=5a, start subscript, 1, end subscript, equals, 5

a_i = a_{i - 1} + 2a

i



=a

i-1



+2a, start subscript, i, end subscript, equals, a, start subscript, i, minus, 1, end subscript, plus, 2

Find the sum of the first 700700700 terms in the sequence.

492,800

Step-by-step explanation:

Given ith term of an arithmetic sequence as shown:

ai = a (i-1) + 2

and a1 = 5

When i = 2

a2 = a (2-1) + 2

a2 = a1+2

a2 = 5+2

a2 = 7

When i = 3

a3 = a (3-1) + 2

a3 = a2+2

a3 = 7+2

a3 = 9

It can be seen that a1, a2 and a3 forms an arithmetic progression

5,7,9 ...

Given first term a1 = 5

Common difference d = 7-5 = 9-7 = 2

To calculate the sum of the first 700 of the sequence, we will use the formula for finding the sum of an arithmetic sequence.

Sn = n/2{2a1 + (n-1) d}

Given n = 700

S700 = 700/2{2 (5) + (700-1) 2}

S700 = 350{10+699 (2) }

S700 = 350{10+1398}

S700 = 350*1408

S700 = 492,800

Therefore, the sum of the first 700 terms in the sequence is 492,800