Question

What is the sum of the first 4 terms of the arithmetic sequence in which the 6th term is 8 and the 10th term is 13?

Answer 1

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 `n^(th)` term is `a+(n-1)d` and sum of first `n` terms is `n/2(2a+(n-1)d)`

Hence `6^(th)` term will be `a+5d=8` and `10^(th)` 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

`4/2*(2*1.75+3*1.25)=2*(3.5+3.75)=2*7.25=14.50`