in the arithmetic sequence: 7, 10, 13, 16 find n if an=6,076​

SOLUTION:Step 1: List the given values.[tex]\begin{aligned} & a_n = 6,076 \\ & a_1 = 7 \\ & a_2 = 10 \\ & a_3 = 13 \\ & a_4 = 16 \end{aligned}[/tex]Step 2: Find the common difference.[tex]\begin{aligned} d & = a_2 - a_1 = a_3 - a_2 = a_4 - a_3 \\ d & = 10 - 7 = 13 - 10 = 16 - 13 \\ d & = 3 = 3 = 3 \end{aligned}[/tex]Step 3: Solve for n.[tex]\begin{aligned} a_n & = a_1 + (n - 1)d \\ 6,076 & = 7 + (n - 1)(3) \\ 7 + (n - 1)(3) & = 6,076 \\ 3(n - 1) & = 6,076 - 7 \\ 3(n - 1) & = 6,069 \\ \frac{3(n - 1)}{3} & = \frac{6,069}{3} \\ n - 1 & = 2,023 \\ n & = 2,023 + 1 \\ n & = \boxed{2,024} \end{aligned}[/tex]Hence, the value of n in the arithmetic sequence is 2,024.

Answered by GreatRedSpot | 2024-09-01