Series and Sequence (Binom+AP)

For the following is an A.P.,

1, 3, 5, 7, ...

what is the nth term?

• 2n-1

• 1-2n

• 2n+1

• None of the above.

Given an AP has 5th term equal to 20 and 9th term equal to 8. Find the nth term.

• 32-3n

• 35-3n

• 35-2n

• 32-2n

Which of the following recurrence relation is an AP?

• U_n+1 - U_n=7

• U_n+1 + U_n=7

• U_n+1 - U_n=1+2n

• U_n+1=U_n + 2

Given an AP with first term 8 and common difference d. Find the SUM of the first 10 terms.

• 10(8+10d)

• 10(16+10d)/2

• 10(8+9d)/2

• 10(16+9d)/2

Find 1+4+7+...+(3n-2).

• n(3n-1)/2

• n(3n-2)/2

• n(3n+2)/2

• None of the above.

If we used the binomal series (1-x)^1/2=1-x/2 -x²/8 +... to approximate (17)^1/2 we should let x=

• -16

• 1/18

• -1/16

• -1/18

Which sequence converges?

• 1, - 1/3, 1/9, - 1/27, ...

• 10, 10, 10, 10, ...

• 100, 97, 94, ...

• 2, -2, 2, -2, 2, ...

Which of the following is an AP?

• U_n = n² - 2n

• U_n+1 - U_n = U_n - U_n-1

• U_n+1 - U_n = 2n-1

• None of the above