Question 89

The 3rd and 8th term of an arithmetic progression are -13 and 2 respectively. What is the 14th term?

Solution

Let the first term of an AP = $$a$$ and the common difference = $$d$$

3th term of AP = $$A_3=a+2d=-13$$ ----------(i)

8th term = $$A_8=a+7d=2$$ --------(ii)

Subtracting equation (i) from (ii), we get :

=> $$7d-2d=2-(-13)$$

=> $$5d=15$$

=> $$d=\frac{15}{5}=3$$

Substituting it in equation (ii), => $$a=2-7(3)=2-21=-19$$

$$\therefore$$ 14th term = $$A_{14}=a+13d$$

= $$-19+13(3)=-19+39=20$$

=> Ans - (C)

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