Mixed AP constraints

Problem Statement

An arithmetic sequence has $a_3=11$ and $a_{12}=47$. Find $a_1$ and $d$, then determine $S_{25}$.

Solutions

Use $a_n=a+(n-1)d$:

Subtract:

then $a=11-8=3$. Now

so

Further Readings

• HSC Sequences: https://vumaths.com/booklets/hsc-sequences/
• HSC Mechanics: https://vumaths.com/booklets/hsc-mechanics/
• HSC Collections: https://vumaths.com/booklets/hsc-collections/
• HSC Trigonometry: https://vumaths.com/booklets/hsc-trigonometry/

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