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)

Tammy Todd

Tammy Todd

Answered question

2021-01-31

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)

Answer & Explanation

likvau

likvau

Skilled2021-02-01Added 75 answers

Step 1 Let A1,A2,A3,A4,A5 be five arithmetic means between 5 and 21. Then 5,A1,A2,A3,A4,A5,21 are in arithmetic sequence with first term and seventh term are a1=5,
a7=21 Step 2 Now nth term of arithmetic sequence is an=a1+(n1)d For n=7, a7a1+(71)d
21=5+6d
6d=215
6d=16 d=73 Step 3 Therefore, the five arithmetic means between 5 and 21 are A1=a1+d=5+83=233
A2=a1+2d=5+2×83=313
A3=a1+3d=5+3×83=393=13
A4=a1+4d=5+4×83=473
A5=a1+5d=5+5×83=553 Step 4 Ans:The five arithmetic means between 5 and 21 are 233,313,13,473,553

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