2) The algebraic form of an arithmetic sequence is 7n + 3. a) What is the common difference? b) What is the first term of this sequence ? c) What is the position of 171in this sequence? d) What is the position of248in this sequence ? e) How many terms are there from 171 to 248 in this sequence?
Answers
Answer:
To find the "nth" term of an arithmetic sequence, start with the first term, a(1). Add to that the product of "n-1" and "d" (the difference between any two consecutive terms). For example, take the arithmetic sequence 3, 9, 15, 21, 27.... a(1) = 3. d = 6 (because the difference between consecutive terms is always 6
Answer:
Step-by-step explanation:
Tn = a + (n - 1)d
Tn = a + dn - d
Tn = dn + (a - d) .........1
Tn = 7n + 3...........2
Comparing eqn. 1 and 2
a) dn = 7n
Therefore,
d = 7
b) a - d = 3
a - 7 = 3
a = 7 + 3
a = 10
c) Tn = a + (n - 1)d = 171
10 + (n - 1)7 = 171
10 + 7n - 7 = 171
3 + 7n = 171
7n = 171 - 3
7n = 168
n = 24th term
d) Tn = a + (n - 1)d = 248
Tn = 10 + (n - 1)7 = 248
10 + 7n- 7 = 248
3 + 7n = 248
7n = 248 - 3
7n = 245
n = 35th term
e) 35 - 24
= 11 numbers between them