Question

Find the 17th term in the sequence for which a1 = 10 and d = -3.

a. -42
c. 24
b. 34
d. -38

Answer 1

Rule to find
`n`-th element of arithmetic sequence:

`x_(n)=a_(1)+d(n-1)`

So for
`n=17`:

`x_(n)=10+(-3)*(17-1)=10+(-3)*16=10-48=-38`

Answer 2

Answer: (d) -38 is the correct option.

Step-by-step explanation: We are given to find the 17th term of a sequence with first term a(1) = 10 and common difference, d = -3.

Since common difference exists between any two consecutive terms of the sequence, so the given sequence is ARITHMETIC.

We know that

the n-th term of an arithmetic sequence with first term a(1) and common difference d is given by

`a(n)=a(1)+(n-1)d.`

Therefore, the 17-th term of the given arithmetic sequence will be

`a(17)=a(1)+(17-1)* d=10+16*(-3)=10-48=-38.`

Thus, the 17-th term of the given sequence is -38.

Option (d) is CORRECT.