Identify the 42nd term of an arithmetic sequence where a1 = −12 and a27 = 66
The arithmetic formula is expressed as an = a1 + d (n-1)where n is an integer. Substituting from the given a1 = -12 and a27 = 66, 66 = -12 + d (27-1). hence , d is equal to 3. a42 thus using the formula is equal to 111. The final answer to this problem is 111.
a1 = -12
a27= 66
the formula of a27 is "a1 + 26d"
so
a1+26d= 66
-12 +26d=66
26d=78
d=3
now, the formula of "a42=a1+41d"
a42= a1+41d
a42= -12 + 41*3
a42= 111