Question

Find the sum of the first 10 positive integers
Is it 110?

Which term of the arithmetic sequence is 25?
-2,1,4,...
Is it 70?

Which term of the arithmetic sequence is177?
2,9,16,...
Is it 1234?

Find the sum of the first 8 positive odd integers.
Is it 64?

Answer 1

#1, wrong
1+2+..+8+9+10
= (10/2)(first + last) = 55

#2. wrong
a=-2 , d = 3, term(n) = 25
term(n) = a + (n-1)d
25 = -2 + 3(n-1)
27 = 3n - 3
30 = 3n
n = 10 , so it is the 10th term

#3. wrong
a=2, d = 7, term(n) = 177
177 = 2 + 7(n-1)
175 = 7n - 7
182 = 7n
n = 26 , so the 26th term

#4. yeah, you got one right.
1+3+5+... for 8 terms
a=1, d=2, n=8
sum(8) = (8/2)(2 + 7(2)) = 64
or
notice:
sum(1) = 1 = 1^2
sum(2) = 4 = 2^2
sum(3) = 9 = 3^2
sum(4) = 16 = 4^2
so sum(8) = 8^2 = 64