I have no idea how to find a (the first term) or d (the common difference between two successive pairs of terms).
Could someone please explain how to solve this please? Thanks.
The sum of the first two terms of an arithmetic sequence is 16. The sum of the second and third terms is 28. What are the first three terms of the sequence?
+128475 Let a1 be the first term
Then the second term is a1 + d
And the third term is a1 + 2d
So we have
a1 + [ a1 + d ] = 16 → 2a1 + d = 16 → d = 16 - 2a1 (1)
[a1 + d] + [a1 + 2d] = 28 → 2a1 + 3d = 28 (2)
Sub (1) into (2) and we have
2a1 + 3 [16 - 2a1] = 28
-4a1 + 48 = 28 subtract 48 from both sides
-4a1 = -20 divide both sides by -4
a1 = 5
And using (1).....d = 16 - 2(5) = 16 - 10 = 6
So the first term = 5
The second term is 11
And the third term = 17
