# Find the sum of first 20 terms of the arithmetic series in which 3rd term is 7 and 7th term is 2 more than three times its 3rd term.

First term = a

Common difference = d

3rd term = a + (3–1)d = a + 2d

7th term = a + (7–1)d = a + 6d

Now, 3rd term = 7

a + 2d = 7 ………………………(1)

And, 7th term = 3 × (3rd term) + 2

a + 6d = 3(a + 2d) + 2

a + 6d = 3a + 6d + 2

2a = –2

a = –1

Putting value of a in (1)

( –1) + 2d = 7

2d = 8

d = 4

Sum of terms = Sum of terms = Sum of terms = Sum of terms = 740

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Interactive Quiz:Euclid's Division Lemma44 mins  Champ Quiz | Fundamental Principle Of Arithmetic41 mins  Fundamental Theorem of Arithmetic-238 mins  Fundamental Theorem of Arithmetic- 143 mins  Quiz | Imp Qs on Real Numbers37 mins  NCERT | Imp. Qs. on Rational and Irrational Numbers44 mins  Euclids Division Lemma49 mins  Interactive Quiz - HCF and LCM32 mins  Relation Between LCM , HCF and Numbers46 mins  Application of Euclids Division Lemma50 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 