-121,-117,-113,... How many terms are there if -1601 is the last number?​

SOLUTION:Step 1: List the given values.[tex]\begin{aligned} & a_n = 1,603 \\ & a_1 = -121 \\ & a_2 = -117 \\ & a_3 = -113 \end{aligned}[/tex]Step 2: Find the common difference.[tex]\begin{aligned} d & = a_2 - a_1 = a_3 - a_2 \\ d & = -117 - (-121) = -113 - (-117) \\ d & = -117 + 121 = -113 + 117 \\ d & = 4 = 4 \end{aligned}[/tex]Step 3: Solve for the number of terms.[tex]\begin{aligned} a_n & = a_1 + (n - 1)d \\ 1,603 & = -121 + (n - 1)(4) \\ -121 + (n - 1)(4) & = 1,603 \\ 4(n - 1) & = 1,603 + 121 \\ 4(n - 1) & = 1,724 \\ \frac{4(n - 1)}{4} & = \frac{1,724}{4} \\ n - 1 & = 431 \\ n & = 431 + 1 \\ n & = \boxed{432} \end{aligned}[/tex]Hence, there are 432 terms.

Answered by GreatRedSpot | 2024-09-06