1) Given the terms a35 = 1238 and a70 = 1483 of an Arithmetic. Find the exact value of the term a105 a sequence and sum of sequence.

2) Given a3 = 99 and a5 = 891 of a Geometric. Find the exact value of the term a7 of the sequence and the sum of sequence.

1.

a+ 34d = 1238
a+69d = 1483
subtract them
35d = 245
d = 7
then in the 1st equation:
a + 238 = 1238
a = 1000
so term(105) = 1000 + 104(7) = 1728

2.
ar^2 = 99
ar^4 = 891
divide the 2nd by the third.
r^2 = 9
r = ±3
in the 1st
a(9) = 99
a = 11

then term(7)
= ar^6
= 11(3)^6 = 8019

Thanks a lot

An arithmetic sequence is represented in the following table. Enter the missing term of the sequence.

Math-ariyhmetic & geometric

To find the exact value of the term a105 in an arithmetic sequence, we need to find the common difference (d) and the formula for finding the nth term of an arithmetic sequence.

Given a35 = 1238 and a70 = 1483, we can use these terms to find the common difference (d):
d = a70 - a35
d = 1483 - 1238
d = 245

Now that we know the common difference, we can use the formula for finding the nth term of an arithmetic sequence:
an = a1 + (n-1)d

Substituting the values, we have:
a105 = a1 + (105-1) * d

To find the exact value of a105, we need the value of a1, which is not provided in the given information. We cannot find the exact value of a105 without knowing a1.

Similarly, to find the sum of the arithmetic sequence, we need the value of a1. So, without the value of a1, we can't determine the exact sum of the sequence.

Moving on to the second question:

To find the exact value of term a7 in a geometric sequence, we need to find the common ratio (r) and use the formula for finding the nth term of a geometric sequence.

Given a3 = 99 and a5 = 891, we can find the common ratio (r):
r = a5/a3
r = 891/99
r = 9

Now that we know the common ratio, we can use the formula for finding the nth term of a geometric sequence:
an = a1 * r^(n-1)

Substituting the values, we have:
a7 = a1 * 9^(7-1)

We still need the value of a1 to find the exact value of a7. Without knowing a1, we cannot determine the exact value of a7.

For the sum of the geometric sequence, we can use the formula:
S = (a1 * (r^n - 1)) / (r - 1)

Again, without the value of a1, we cannot determine the exact sum of the sequence.