Math, asked by aadhilahamed9172, 4 days ago

The sum of the 8th and the 9th terms of an arithmetic sequence is 40 .
a) What is the sum of the first and the 16th terms of this sequence ?
b) What is the sum of the first 16 terms of this sequence ?​

Answers

Answered by akshat5926
2

Answer:

a) 40

b) 320

Step-by-step explanation:

a8 + a9 = 40

a + 7d + a + 8d = 40

2a + 15 d = 40

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a)   a = 40 - 15d/2

a + a16 = (40 - 15d/2) + (40 - 15d/2) + 15 d

           = 40 - 15d/2 + 40 - 15d/2 + 15d

           = 40 - 15d + 15d

           = 40

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b)  n = 16

    a = 40-15d/2

    a16 = 40-15d/2 + 15d

s16 = 16/2 [40-15d/2 + (40-15d/2 + 15d)]

     = 8 (40-15d/2 + 40 - 15d/2 + 15d)

     = 8(40)

     = 320

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