Progressions : Sum of terms of 2 A.P. Sequences

Question

The sum of the first 50 terms common to the Arithmetic Sequence 15, 19, 23..... and the Arithmetic Sequence 14, 19, 24..... is.

1. 25450
2. 24550
3. 50900
4. 49100
   
   

Correct Choice is (1) and Correct Answer is 25450

Explanatory Answer

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 =

Hence, the sum of first 50 terms of this sequence = = 25450.

---

More Questions on Arithmetic and Geometric Progressions

CAT Practice Questions and Answers : Listed Topicwise

Number Theory		Permutation & Probability		Data sufficiency		Inequalities
Geometry		Mensuration		Trigonometry		Coordinate Geometry
Percentages		Profit Loss		Ratio Proportion		Mixtures Alligation
Speed Time Distance		Pipes Cisterns		Linear Quadratic		Races
Progressions, AP & GP		New Topic		New Topic		New Topic