# if the 6th term of AP is -10 and its 10th term is -26 then find the 15th term of the AP

if the 6th term of AP is -10 and its 10th term is -26 then find the 15th term of the AP

### Given:

• the 6th term of AP is -10
• 10th term is -26

### To find:

• the 15th term of the AP

### Solution:

Let a be the first term and d be the common difference of the given AP. Then,

$$\sf \: T_6=-10 \\ \\ \sf \implies \: a – 5d = – 10 \: \: – – – – – (i)$$

$$\sf \: T_10=-26 \\ \\ \sf \implies \: a + 9d = – 26 \: \: \: \: \: – – – – (ii)$$

On subtracting (I) from (ii)

$$\sf \: 4d=(-26+10) \\ \\ \sf \implies4d=-16 \\ \\ \sf \implies d = \cancel \frac{ – 16}{4} \\ \\ \sf \implies \: d=-4$$

Putting d = 4 in (I)

$$\sf \: a+5d=-10 \\ \\ \sf \implies \: a+5×(-4)=-10 \\ \\ \sf \implies \: a – 20 = – 10 \\ \\ \sf \implies \: a = – 10 + 20 \\ \\ \sf \implies \: a = 10$$

Now the 15th term of this AP

$$\sf \: T_{15}=a+(15-1)d \\ \\ \sf \: = a + 14d \\ \\ \sf = 10 + 14 \times ( – 4) \\ \\ \sf = 10 – 56 \\ \\ \sf = – 46$$