NUS high school mathematics scholarship

Algebra Level 2

A sequence $T_n$ is given as: $T_{1}=7;T_{2}=13;T_{3}=19;T_{4}=25$ such that the difference between every two consecutive terms is the same.

Find the value of $T_{1}+T_{2}+T_{3}+\cdots+T_{50}$ .

1 solution

Sam Bealing
Apr 26, 2016

By calculation we get $T_2-T_1=T_3-T_2=T_4-T_3=6$ so we assume:

$T_n=6n+1$

$\sum_{i=1}^{50} T_i=\sum_{i=1}^{50} 6n+1=6 \sum_{i=1}^{50} n+ \sum_{i=1}^{50} 1$

$...=6 \dfrac{50(50+1)}{2}+50=7650+50=\boxed{7700}$

Note: I've used $\sum_{i=1}^{n} i= \dfrac{n(n+1)}{2}$ .

Simple standard approach.

There's a typo in your note.

Aditya Kumar - 5 years, 1 month ago

Fixed thank you.

Sam Bealing - 5 years, 1 month ago