Question

35th partial sum of the arithmetic sequence with terms aₙ = n/2 + 1 ??​

Answer 1

Step-by-step explanation:

an=n/2+1

a35=35/2+1

a35=17.5+1

a35=18.1

a=18.1/35

0.51

Answer 2

Answer:

35th partial sum of the arithmetic sequence with terms aₙ = n/2 + 1 be 350

Step-by-step explanation:

Hint:

The 35th partial sum of this sequence is the sum of the first thirty-five terms.

nth term aₙ = a+(n-1)d

sum of n terms sₙ=n/2(first term +last term)

The first few terms of the sequence are:

$\begin{aligned}&a_{1}=1 / 2+1=3 / 2 \\&a_{2}=2 / 2+1=2 \\&a_{3}=3 / 2+1=5 / 2\end{aligned}$

Here common difference

$d=second term - first term \\ d=a_{2} -a_{1}\\ = 2-\frac{3}{2} \\ =\frac{1}{2}$

$a_{35}=a_{1}+(35-1) d=\frac{3}{2}+34 \times(\frac{1}{2})=17 / 2 Now, the sum =(35 / 2) \times(3 / 2+37 / 2) \begin{aligned}&=(35 / 2) \times(40 / 2) \\&=(35 / 2) \times 20 \\&=35 \times 10 \\&=350\end{aligned}$