A)the eight term of arthematic sequence is 28, the common difference is 6 calculate the first term of sequence. b) the sum of first n term is 760calculate the vale of n.

Solution

Part A

The general form of the n-th term = a + (n-1)d

Here we are given the 8th term A8 = 28 , common difference (d) = 6

A8 = a + (n - 1) 6

28 = a + (8- 1)6

28 = a + 7*6

28 = a + 42

a = 28 - 42

a = -14

Part B

n-th term  is 760. a = -14 and d = 6.

Plugging in the values in the general form, we get

760 = -14 + (n -1)6

760 = -14 + 6n - 6

760 = -20 + 6n

6n = 760 + 20

6n = 780

Dividing both sides by 6, we get

n = 780/6 = 130

The value of n is 130

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