Question

The sum of the first $50$ terms common to the Arithmetic Sequence $15,19,\mathrm{23.....}$ And the Arithmetic Sequence $14,19,24...$ is

• A. $25450$
• B. $24550$
• C. $50900$
• D. $49100$

Answer 1

The correct option is A $25450$

The two series are in A.P. Therefore, the common series will also be in an A.P
Common difference of 1st series $=4$ and the common difference of 2nd series $=5$.
Common difference of the sequence whose terms are common to the two series is given by L.C.M of 4 and 5 $=20$
Here the first term of the identical (common terms) sequence is 19.
We know the sum of first $n$ terms is given by = $\frac{n}{2}[2a+(n+1\left)d\right]$
Hence, the sum of first $50$ terms of this sequence = $\frac{50}{2}[2\times 19+(50+1\left)20\right]=25450$.