Question

The sum of first 13 terms of an ap is 390 find the 7th term

Answer 1

Answer:

a7 = a + 6d.....(1)

S13 = 390

390 = 13/2(2a + 12d)

60 = 2a + 12d

divide 2 on both sides

30 = a + 6d

a7 = 30. from. (1)

.•. seventh term is 30.

Hope this answer may help you....

Answer 2

Answer:

7th term of the AP = 30

Step-by-step explanation:

Given,

The sum of the first 13 terms of an AP = 390

To find,

The 7th term of the AP

Solution:

Recall the formula

nth term of an AP =aₙ = a+(n-1)d --------------------(1)

Sum to n-terms of an AP = Sₙ= $\frac{n}{2}$[2a+(n-1)d] ---------------(2)

where 'a' is the first term and 'd' is the common difference of the AP

Since it is given that the sum of the first 13 terms of the AP = 390, we have

S₁₃ = 390

Substituting n = 13 in equation (2) we get,

$\frac{13}{2}$[2a+12d] = 390

$\frac{13}{2}$×2[a+6d] = 390

13×(a+6d) = 390

a+6d = $\frac{390}{13}$ = 30

a+6d = 30 -----------------------(3)

Again, we need to find the seventh term of the AP

substituting n = 7 in equation (1) we get

7th term of the AP = a₇ = a+(7-1)d = a+6d

From equation (3) we have a+6d = 30

∴7th term of the AP = 30

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