Respuesta :
Answer: a21 = 65
Step-by-step explanation: to find the common difference (d) of an arithmetic sequence when given the first term (a1) and a later term (a5), we can use the formula:
a5 = a1 + 4d
given that a1 = 5 and a5 = 17, we can plug these values into the formula and solve for d: 17 = 5+4d subtracting 5 from both sides: 17-5 =4d ---> 12 = 4d. dividing both sides by 4: 12/4 = d --> d =3.
Now, to find the 21st term of the sequence, we can use the formula for the n term for an arithmetic sequence:
an = a1 + (n-1 d
given a1 = 5, d = 3, and n = 21, we can plug these values into the formula:
a21 = 5 + (21 - 1) x 3
a21 = 5 +20 x 3
a21 = 5 + 60
a21 = 65
so, the 21st erm of the sequence is a21 = 65.
therefore, the common difference is d = 3 and the 21st term of the seqence is a21 = 65.
