Question

the first term of an arithmetic sequence is 1 and the sum of the first terms is 100. find the first four terms

Answer 1

Answer:

Sum of the first 4 terms is 14.50

Explanation:

In an arithmetic sequence, whose first term is a and difference between a term and its preceding term is d,

the nth term is a+(n−1)d and sum of first n terms is n2(2a+(n−1)d)

Hence 6th term will be a+5d=8 and 10th term will be a+9d=13

Subtracting first from second, 4d=5 or d=1.25

and a=8−5⋅1.25=8−6.25=1.75

Hence sum of first four terms is

42⋅(2⋅1.75+3⋅1.25)=2⋅(3.5+3.75)=2⋅7.25=14.50