Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest
hundredth.
-$\mathrm { S } _ { 9 } = 369$, a $9 = 77$
A) $\mathrm { a } _ { 1 } = 5 , \mathrm {~d} = 9$
B) $\mathrm { a } _ { 1 } = - 611 , \mathrm {~d} = 9$
C) $a _ { 1 } = 5 , d = 17.11$
D) $\mathrm { a } _ { 1 } = - 611 , \mathrm {~d} = 17.11$

Question

Quizplus · Accepted Answer

The sum of the first 9 terms $ S_9 = 369 $ and the 9th term $ a_9 = 77 $. Using the formula for the sum of an arithmetic sequence $ S_n = \frac{n}{2} (2a_1 + (n-1)d) $ and the formula for the nth term $ a_n = a_1 + (n-1)d $, we can solve for $ a_1 $ and $ d $. Solving these equations gives $ a_1 = 5 $ and $ d = 9 $.

Find the First Term and the Common Difference for the Arithmetic