Find the 100th term of the arithmetic sequence with first te

Find the 100^th term of the arithmetic sequence with first term 2 and eight term 23 Part B Find the sum of the first 34 terms of the arithmetic sequence with first term 4 and 34^th term 70

Solution

nth term of AP is given by:

an = a1 + (n - 1)*d

a1 = first term = 2

a8 = eighth term = 23

So,

23 = 2 + (8 - 1)*d

d = 21/7 = 3

Now, 100th term will be

a100 = 2 + (100 -1)*3 = 299

B.

a1 = 4

a34 = 70

sum of AP is given by:

S = (n/2)*[a1 + a34]

S = (34/2)*[4 + 70] = 1258