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# In an arithmetic sequence whose 4th term is 14 and whose 11th term is 70, the fi...

### Question

In an arithmetic sequence whose 4th term is 14 and whose 11th term is 70, the first term and common difference are

### Options

A) a = -10, d = 8

B) a = -7, d = 7

C) a = 10, d = 8

D) a =-14, d = 7

### Explanation:

$$a_4 = a+3d = 14$$ ..... (1)
$$a_{11} = a+10d = 70$$ ..... (2)
Solve simultaneously, subtract equation (1) from (2)
$$7d = 56$$
$$d = \cfrac{56}{7} = 8$$
$$a+3(8)=14$$
$$a=14-24=-10$$

## Discussion (2)

• $$a_4 = a+3d = 14$$ ..... (1)
$$a_{11} = a+10d = 70$$ ..... (2)
Solve simultaneously, subtract equation (1) from (2)
$$7d = 56$$
$$d = \cfrac{56}{7} = 8$$
$$a+3(8)=14$$
$$a=14-24=-10$$