The 6th term of an Arithmetic progression is -10 and its 10th term is -26. Determine 15th term of an Arithmetic progression

### Asked by thakurayush007700 | 8th May, 2020, 10:39: AM

Expert Answer:

###
Let a and d be the first term and common difference of an AP
It is given that, 6^{th} term a_{6} = -10 and 10^{th} term a_{10} = -26.
Therefore,
a + 5d = -10 ... (i)
a + 9d = -26 ... (ii)
Subtracting (i) from (ii), we have
4d = -16
d = -4
Substituting in (i), we have
a + 5(-4) = -10
a = -10+20 = 10
15^{th} term is a_{15} = a + 14d = 10 + 14(-4) = 10 - 56 = -46
Hence, the 15^{th} term is -46.

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

It is given that, 6

^{th}term a_{6}= -10 and 10^{th}term a_{10}= -26.Therefore,

a + 5d = -10 ... (i)

a + 9d = -26 ... (ii)

Subtracting (i) from (ii), we have

4d = -16

d = -4

Substituting in (i), we have

a + 5(-4) = -10

a = -10+20 = 10

15

^{th}term is a_{15}= a + 14d = 10 + 14(-4) = 10 - 56 = -46Hence, the 15

^{th}term is -46.### Answered by Renu Varma | 8th May, 2020, 11:11: AM

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