Insert five arithmetic means between 5 and 21. (Enter your answers from smallest to largest.) Find the sum of the first n terms of the arithmetic sequence. −9 + (−12) + (−15) + . (to 10 terms)

Step 1 Let A 1 , A 2 , A 3 , A 4 , A 5 be five arithmetic means between 5 and 21. Then 5 , A 1 , A 2 , A 3 , A 4 , A 5 , 21 are in arithmetic sequence with first term and seventh term are a 1 = 5 ,
a 7 = 21 Step 2 Now nth term of arithmetic sequence is a n = a 1 + ( n − 1 ) d For n = 7 , a 7 − a 1 + ( 7 − 1 ) d
21 = 5 + 6 d
6 d = 21 − 5
6 d = 16 d = 7 3 Step 3 Therefore, the five arithmetic means between 5 and 21 are A 1 = a 1 + d = 5 + 8 3 = 23 3
A 2 = a 1 + 2 d = 5 + 2 × 8 3 = 31 3
A 3 = a 1 + 3 d = 5 + 3 × 8 3 = 39 3 = 13
A 4 = a 1 + 4 d = 5 + 4 × 8 3 = 47 3
A 5 = a 1 + 5 d = 5 + 5 × 8 3 = 55 3 Step 4 Ans:The five arithmetic means between 5 and 21 are 23 3 , 31 3 , 13 , 47 3 , 55 3

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