Question

if the sum of first 7 terms of AP is 49 and sum of first 17 terms is 289 then find the sum of n terms of AP

Answer 1

Step-by-step explanation:

hope it helps you.......... .

Answer 2

Given:

Sum of first 7 terms of an AP is 49.

Sum of 17 terms is 289.

To Find:

What is sum of first n term of AP?

Solution: As we know that sum of n terms of an AP is given by

Sⁿ = n/2{2a + (n – 1)d}

Here,

Sum of first 7 terms is 49.

➡ S⁷ = 7/2{2a + (n – 1)d}

➡49 = 7/2{2a + (7 – 1)d}

➡ 49 × 2 = 7{2a + 6d}

➡ 98 = 14a + 42d

➡ 98 = 14(a + 3d)

➡98/14 = a + 3d

➡ 7 = a + 3d

➡7 – 3d = a......(i)

Sum of 17 terms is 289

➡ 289 = 17/2{2a + (17 – 1)d}

➡ 289 × 2 = 17{2a + 16d}

➡ 578 = 34a + 272d

➡ 578 = 34(a + 8d)

➡ 578/34 = a + 8d

➡ 17 = a + 8d......(ii)

Now put the value of a in equation 2 from 1.

⟹ 17 = 7 – 3d + 8d

⟹ 17 – 7 = 5d

⟹ 10 = 5d

⟹ 2 = d

Putting the value of d in equation 1.

⟹ 7 – 3(2) = a

⟹ 7 – 6 = a

⟹ 1 = a

Now, sum of n term of AP will be

Sⁿ = n/2{2 × 1 + (n – 1)2}

n/2{2 + (2n – 2}

n/2 × 2n

n²

Hence, sum of n term of AP will be n².

NOTE

• Sum = n²