+17 The 80th term of an arithmetic sequence is twice the 30th term. If the first term of the sequence is 7, what is the 40th term?
+37159 Find 'd' the common difference :
From a1 to a30 is 30 terms ( 29 d's)
From 30 to 80 is fifty d's
7 + 29 d = value of 30th term
then for the 80th term (7+29d) + 50 d = 2( 7 + 29 d )
7 + 79 d = 14 + 58 d
-7 = -21 d
d = 1/3 a1 = 7 then a30 = 16 2/3 a80 = 33 1/3 Check !
So 40th term 7 + 39 ( 1/3) = 20
+37159 Find 'd' the common difference :
From a1 to a30 is 30 terms ( 29 d's)
From 30 to 80 is fifty d's
7 + 29 d = value of 30th term
then for the 80th term (7+29d) + 50 d = 2( 7 + 29 d )
7 + 79 d = 14 + 58 d
-7 = -21 d
d = 1/3 a1 = 7 then a30 = 16 2/3 a80 = 33 1/3 Check !
So 40th term 7 + 39 ( 1/3) = 20
