Question

10th term if an ap is 91 . if its 6th term of an ap is 43 then find the sum of its first 10 terms​

Answer 1

I know that you know that I know did you know

Answer 2

SOLUTION

GIVEN

• 10th term if an AP is 91

• 6th term of an AP is 43

TO DETERMINE

The sum of its first 10 terms

EVALUATION

Let a be the First term and d be the Common Difference of the Arithmetic progression

Then

10th term = a + 9d

6th term = a + 5d

So by the given condition

$\sf{a + 9d = 91 \: \: \: \: \: \: - - - - (1)}$

$\sf{a + 5d = 43 \: \: \: \: \: \: - - - - (2)}$

Equation 1 - Equation 2 gives

$\sf{4d = 48 \:}$

$\implies \sf{d = 12}$

Equation 1 gives a = - 17

Hence the required sum of first 10 terms

$\displaystyle \sf{ = \frac{n}{2} \bigg[ 2a + (n - 1)d\bigg]}$

$\displaystyle \sf{ = \frac{10}{2} \bigg[ - 34 + 9d\bigg]}$

$\displaystyle \sf{ = \frac{10}{2} \bigg[ - 34 +108\bigg]}$

$\displaystyle \sf{ = 5 \times 74}$

$\sf{ = 370}$

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