The sum of the fourth and sixth term of an arithmetical progression is 42.the sum of the third and the ninth term is 52.find the first term,the common difference and the sum of the first tenth term of the progression.

Question

The sum of the fourth and sixth term of an arithmetical progression is 42.the sum of the third and the ninth term is 52.find the first term,the common difference and the sum of the first tenth term of the progression.

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1 answer
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Answer 1

R_scott answered
3 years ago

4 a + 3 d + 6 a + 5 d = 42 ... 10 a + 8 d = 42 ... 5 a + 4 d = 21

3 a + 2 d + 9 a + 8d = 52 ... 12 a + 10 d = 52 ... 6 a + 5 d = 26

30 a + 24 d = 126

30 a + 25 d = 130

subtracting equations ... d = 4
... so , a = 1