Question

sum of first 5 term is 320 and sum of next 5 term is 395 what is the 1st term ​

Answer 1

Answer:

Here is your answer.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

We know that,

S(nth) = (n/2)[2a + (n - 1)d]

Now,

Sum of first 5 terms

where n = 5, 1st term = a, common difference = d

S(5th) = (5/2)[2a + (5 - 1)d]

S(5th) = (5/2)[2a + 4d]

S(5th) = (5/2) × 2[a + 2d]

S(5th) = 5 × (a + 2d)

S(5th) = 5a + 10d ------ 1

320 = 5(a + 2d)

320/5 = a + 2d

64 = a + 2d ----- 2

Sum of the next 5 terms will be,

S(10th) - S(5th) = 395 ------- 3

Now,

S(10th) = (10/2)[2a + (10 - 1)d]

S(10th) = 5(2a + 9d)

S(10th) = 10a + 45d ------ 4

Now, from eq.1, eq.3 and eq.4, we get

S(10th) - S(5th) = 395

10a + 45d - (5a + 10d) = 395

10a + 45d - 5a - 10d = 395

5a + 35d = 395

5(a + 7d) = 395

a + 7d = 395/5

a + 7d = 79 ------ 5

Subtracting eq.2 and eq.5 we get

a + 7d - (a + 2d) = 79 - 64

a - a + 7d - 2d = 15

5d = 15

d = 15/5

d = 3

Putting d = 3 in eq.1 we get

a + 2(3) = 64

a = 64 - 6

a = 58

Thus, the first term is 58

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