Question

Please help me solve this please​

Answer 1

Answer:-

The Sum Of First 15 Terms of The A.P. will be 0.

Explanation:-

Given:-

• First Term $\tt(a)$ = 14.

• Second Term $\tt(a_2)$ = 12.

So,

• Let the common difference of the given AP be d.

• The number of terms be n.

Formulas Used:-

$\\ \large\bf\leadsto S_n = \dfrac{n}{2}\bigg[2a+(n-1)d\bigg].$

$\\ \large\bf\leadsto d = a_2-a.$

Where,

• $\bf S_n$ = Sum of n terms.

Solution:-

By Formula we get,

$\\ \bf\mapsto d = 12 - 14 = - 2$

In the question it is given that sum is 0.

$\\ \tt\mapsto S_n = 0$

$\\ \tt\mapsto \frac{n}{2} \bigg[2a + (n - 1)d \bigg] = 0.$

$\\ \tt\mapsto \frac{n}{2} \bigg[2(14) + (n - 1)( - 2) \bigg] = 0.$

$\\ \tt\mapsto n \bigg[28 - 2n + 2 \bigg] = 0 \times 2.$

$\\ \tt\mapsto n \bigg[28 - 2n + 2 \bigg] = 0.$

$\\ \tt\mapsto 28 + 2 - 2n = \dfrac{0}{n}.$

$\\ \tt\mapsto 28 + 2 - 2n = 0.$

$\\ \tt\mapsto30 - 2n = 0.$

$\\ \tt\mapsto2n = 30.$

$\\ \tt\mapsto n = \frac{30}{2} .$

$\\ \red{ \large{\bf\mapsto{ \underline {\boxed{ \blue{ \bf n = 15.}}}}}}$

So the required number of terms is n which is equal to 15.

$\bf\therefore$ The Sum Of First 15 Terms Of The Given A.P. Will Be 0.