Question

The sum of 8th term and 23rd term of arithmetic sequence is 75 a) Find 1st term + 30th term b) Find 5th term + 26th term​

Answer 1

Answer:

Given an arithmetic sequence with the first term a1 and the common difference d , the nth (or general) term is given by an=a1+(n−1)d .

Example 1:

Find the 27th term of the arithmetic sequence 5,8,11,54,... .

a1=5,  d=8−5=3

So,

a27=5+(27−1)(3)        =83

Example 2:

Find the 40th term for the arithmetic sequence in which

a8=60 and a12=48 .

Substitute 60 for a8 and 48 for a12 in the formula

an=a1+(n−1)d to obtain a system of linear equations in terms of a1 and d .

a8=a1+(8−1)d→60=a1+7da12=a1+(12−1)d→48=a1+11d

Subtract the second equation from the first equation and solve for d .

12=−4d−3=d

Then 60=a1+7(−3) . Solve for a .

60=a1−2181=a1

Now use the formula to find a40 .

a40=81+39(−3)=81−117