Select the answers that best complete the given statements. A sequence in which each term after the first differs from the preceding term by a constant amount is called alan (1) sequence. The difference between consecutive terms is called the (2) of the sequence. (1) O arithmetic (2) O common difference O addition term geometric O constant factor 2. Select the answers that best complete the given statements. The sum, So, of the first n terms of an arithmetic sequence is given by the formula S, = (1) In the formula for S,, a, is the (2) In the formula for S,, a, is the (3) (1) O = ( a, + an). (2) O first term, (3) Onth term. second term. first term. 00 O 7 (21 + an) . last term. second term. O nth term O last term. O z (an - 21 ) . Write the first six terms of the arithmetic sequence with the given first term, a, , and common difference, d. ay = 200, d = 10 as a4 =Write the first six terms of the arithmetic sequence shown below. an =an-1+7. 0, 3-4 82 a6 5. Write the first six terms of the arithmetic sequence shown below. an =an-1-8, a1 =27 a2 83 6. Use the formula for the general term (the nth term) of an arithmetic sequence to find the sixth term of the sequence with the given first term and common difference. ay = 16; d= 27. Use the formula for the general term (the nth term) of an arithmetic sequence to find the 50th term of the sequence with the given first term and common difference. 8. =3; d=8 8. Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a, , and common difference, d. Find agg when a, = 38, d= - 2.9. Write a formula for the general term (the nith term) of the arithmetic sequence below. Then use the formula for a,, to find ago, the 20th term of the sequence. 1. 7. 13, 19, ... The formula is an (Simplify your answer.) 10. Write a formula for the general term (the nth term) of this arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find agg, the 20th term of the sequence. a, - - 18, d-5 Write the formula for the general term of this arithmetic sequence. an What is the twentieth term of this arithmetic sequence? 11. Write a formula for the general term (the nith term) of the arithmetic sequence shown below. Do not use a recursion formula. Then use the formula for a,, to find azg, the 20th term of the sequence. an = an-1+3. 8, =2 an 320 (Simplify your answer.)12. Find the sum of the first 25 terms of the sequence. 3, 10, 17, 24. ... S26 = 13. Find 1+2+3+4+ ... + 140, the sum of the first 140 natural numbers. The sum is 14. Find the sum of the first 70 positive even integers. The sum is 15. Find the sum of the odd integers between 30 and 52. The sum is 16. Use a system of two equations in two variables, a, and d, to write a formula for the general term (the nth term) of the arithmetic sequence whose fourth term, ay, is 10 and whose ninth term, ag, is 40. 17. A company offers a starting yearly salary of $36,000 with raises of $2,500 per year. Find the total salary over a ten-year period. The total salary is $18. Explain how to find the sum of the first n terms of an arithmetic sequence without having to add up all the terms. Choose the correct answer below. To find the sum of the first in terms of an arithmetic sequence use the formula, O A. S =n(a, -a, ), in which a, is the first term and a, is the nith term. To find the sum of the first n terms of an arithmetic sequence use the formula, JB. S = =(a, + a ), in which a, is the first term and a, is the nth term, To find the sum of the first n terms of an arithmetic sequence use the formula, OC s = =(a, -a), in which a, is the first term and a, is the nith term. To find the sum of the first in terms of an arithmetic sequence use the formula, O D. S =n(a, + a ), in which a, is the first term and a, is the nith term, 19. In the sequence 19300, 20697, 22094, 23491, .... which term is 297303? The term 297303 is the th term.20. Show that the sum of the first n positive odd integers, 1+3+5 + ... + (2n- 1), isn2. The sum, So, of the first n terms of an arithmetic sequence is given by (1) _ in which a, is the first term and a, is the nith term. Substitute the values of a, and a,, into the formula. Sn = (2) (3) Simplify inside the parentheses. (4) (1) O Sn = = (31 - 87) . (2) O n (3) 0 min) (4) O Multiply. 5(1+ (2n - 1)) O Multiply 2 by 2n and add the result to n. O S, =n(a1 - a7) 5(2n) 9 7(1-(1-2n) O Divide. O S, =n(a, + 27). O n(2n - n) O n(0 + n)