how many terms of the series must be added to give a sum of 425?

how many terms of the series must be added to give a sum of 425?|arithmetic, formula, determining

The sum to n terms of an arithmetic series is Sn = n/2(7n +15).

a. How many terms of the series must be added to give a sum of 425?

b. determine the 6th term of the series.
Answer

a. we known that the number of n total terms is 425, so that

Sn = 425

substitution

THAT

we take a positive n value, the number of terms that add up to 425 is n = 10.

b. determine the 6th

determine of a1 :

Formula for determining an arithmetic series is

so, we know value d of formula arithmetic sequence with i = 10:

ai = a1 + d(i - 1)

74 = 11 + d( i - 1 )

74 = 11 + d (10 - 1)

74 = 11 + 9d

9d = 74 - 11

9d = 63

d = 63/9

d = 7

so that, determine the 6th is

a6 = a1 + d(i - 1)

a6 = 11 + 7(6 - 1)

a6 = 11 + 7(5)

a6 = 11 + 35

a6 = 46

that, determine the 6th is 46