Question

The sum of first 7 terms of an ap is 10 and that of next 7 terms is 17 find the first term and common difference

Answer 1

Answer:
1, 8/7, 9/7....
Step-by-step explanation:
Let the first term be A and Common difference be D
We know that Sum of n terms = n/2[2a + (n-1)d], where
n = number of terms, a = first term, d = common difference
Given that Sum of first 7 term = 10
∴ 7/2[2A + 6D] = 10
14A + 42D = 20  ----- ( i )
Also,
Sum of Next 7 terms = 17
Sum of next 7 terms will be Sum of 14 terms - Sum of first 7 terms
∴ [14/2(2A + 13D)] - 10 = 17           [Sum of first 7 terms given 10]
7(2A + 13D) = 27
14A + 91D = 27 ------- ( ii )
Subtracting ( i ) from ( ii )
14A + 91D - (14A + 42D) = 27 - 20
49D = 7
D = 1/7
Putting Value of D in ( i )
14A + 42D = 20
14A + 42(1/7) = 20
14A + 6 = 20
14A = 14
A = 1
∴ First Term is 1 and Common Difference is 1/7
∴ AP is 1, 1+1/7, 1+2/7... or 1, 8/7, 9/7....

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