Question

If two terms of an arithmetic sequence are a11 = 23 and a15 = −5, what is a28?

Answer 1

The value of a28 given a11 = 23 and a15 = −5 is -96

Given:

a11 = 23

a15 = −5

Where,

a1 = first term

d = common difference

a11 = a + 10d = 23

a15 = a + 14d = -5

a + 10d = 23 (1)

a + 10d = 23 (1)a + 14d = -5 (2)

subtract (1) from (2) to eliminate a

14d - 10d = -5 - 23

4d = -28

d = -28 / 4

d = -7

Substitute d = -7 into (1)

a + 10d = 23 (1)

a + 10(-7) = 23

a - 70 = 23

a = 23 + 70

a = 93

So,

a28 = a + 27d

= 93 + 27(-7)

= 93 + -189

= 93 - 189

= -96

Therefore, the value of a28 given a11 = 23 and a15 = −5 is -96

Learn more about arithmetic sequence:

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