Question

The sequence form by common terms of $17,21,\mathrm{25...}\&16,21,26,.....$ has

• A. common difference $20$
• B. sum of first $100$ terms is $1010100$
• C. sum of first $100$ terms is $101100$
• D. tenth term is $201$.

Answer 1

Answer: (A), (C), (D)

common difference $20$
tenth term is $201$.
sum of first $100$ terms is $101100$

The number $21$ appears in both series

The first series is increasing by $5$ and the second by $4$

Thus the common difference is $5\times 4=20$

so keep adding $20$ to find other numbers that appear in both series

thus series $21,41,61,....$

$n^{th}$ term $a_n=a+(n-1)d$

$a=$ First term

$d=$ Common difference

$n=$ number of terms

$a_n=n^{th}$ term

${10}^{th}$ term $=21+(10-1)20$

$=21+180=201$

sum of first $100$ terms $=\frac{n}{2}(2a+(n-1\left)d\right)$

$=50(42+99\times 20)$

$=101100$