The two-digit numbers divisible by 3 range from 12 to 99, forming an AP with common difference 3. There are 30 such numbers and applying the arithmetic sum formula gives a total sum of 1665.
How many 2-digit numbers are divisible by 3? What is the sum of all these 2-digit numbers?
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The two-digit numbers divisible by 3 form the sequence: 12, 15, 18, …, 99.
Here, a = 12, d = 3 and last term tn = 99.
Using tn = a + (n – 1)d:
99 = 12 + (n – 1) x 3
87 = (n – 1) x 3
n – 1 = 29, so n = 30.
There are 30 two-digit numbers divisible by 3.
Their sum is given by Sn = (n / 2) x (a + tn):
S30 = (30 / 2) x (12 + 99) = 15 x 111 = 1665.
Thus, the sum is 1665.
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 8 Predicting What Comes Next: Exploring Sequences and Progressions Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-8/