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

$a(17)=a(1)+(17-1)\times d=10+16\times(-3)=10-48=-38.$

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

Option (d) is CORRECT.