Question

Find the 14th term of an Arithmetic progression 10,-5, -20, ...620.
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Answer 1

Answer:

-185

Step-by-step explanation:

so formula is t(n) = a + (n-1) d

therefore t(14) = 10 + 13 × -15

= 10 -195

= -185

Answer 2

A10 = 41 and a18 = 73

We know that, nth term an

= a + (n – 1)d So, a10

= a + (10 – 1)d ⇒ a + 9d = 41 …… (i)

Similarity, a18 = a + (18 – 1)d ⇒ a + 17d = 73 …… (ii)

Solving (i) and (ii), (ii) – (i)

⇒ a + 17d – (a + 9d) = 73 – 41 8d = 32 ⇒ d = 4

Using d in (i), we get a + 9(4) = 41 a = 41 – 36 = 5

Now, the 26th term is given by a26 = 5 + (26 – 1)4

= 5 + 100 = 105

Therefore the 26th term is 105.