If the sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of the first 10 terms
Solution:
Given, the sum of first 6 terms of an AP is 36
Also, the sum of the first 16 terms of an AP is 256.
We have to find the sum of the first 10 terms.
The sum of the first n terms of an AP is given by
Sₙ = n/2[2a + (n-1)d]
Where, a is the first term
n is the number of terms
d is the common difference
When n = 6,
S₆ = 6/2[2a + (6 - 1)d]
36 = 3[2a + 5d]
2a + 5d = 12 -------------------- (1)
When n = 16,
S₁₆ = 16/2[2a + (16 - 1)d]
256 = 8[2a + 15d]
2a + 15d = 32 ------------------- (2)
Subtracting (1) from (2),
2a + 15d - (2a + 5d) = 32 - 12
2a + 15d - 2a - 5d = 20
15d - 5d = 20
10d = 20
d = 20/10
d = 2
Put d = 2 in (1),
2a + 5(2) = 12
2a + 10 = 12
2a = 12 -10
2a = 2
a = 1
So, the first term, a = 1
Common difference, d = 2
Sum of the first 10 terms, S₁₀ = 10/2[2(1) + (10 - 1)(2)]
= 5[2 + 9(2)]
= 5[2 + 18]
= 5(20)
= 100
Therefore, the sum of the first 10 terms of an AP is 100.
✦ Try This: If the sum of the first 6 terms of an AP is 60 and that of the first 16 terms is 360, find the sum of the first 10 terms
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 28
If the sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of the first 10 terms
Summary:
If the sum of the first 6 terms of an AP is 36 and that of the first 16 terms is 256, then the sum of the first 10 terms is 100.
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