If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
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Answer:
Sum of first 10 terms = 100.
To find :
Sum of first 10 terms
Solution :
Given ,
Sum of n terms = n / 2 [ 2a + (n - 1) d ]
According to the question ,
S6 = 6 / 2 [ 2a + ( 6- 1 ) d ]
36 = 3 ( 2a + 5d )
12 = 2a + 5d → (1)
S16 = 16 / 2 [ 2a + ( 16 - 1 ) d ]
256 = 8 [ 2a + 15d ]
32 = 2a + 15d → (2)
solving equation (1) and (2)
10d = 20
d = 2
a = 1
sum of 10th terms = S10 = 10 / 2 [ 2a + ( 10 - 1 ) d ]
= 5 [ 2 × 1 + 9 × 2 ]
= 5 [ 2 + 18 ]
= 100
∴ Sum of first 10 terms = 100
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