Question

find the number of terms in the AP 10, 4, - 2, - 8,.....,-290 also find its 30 terms from the end​

Answer 1

Step-by-step explanation:

therefore the no of terms is equal to 51

Answer 2

The number of terms in the AP is 51 and 30th term from the end is -56.

Solution:

Given, arithmetic series is 10, 4, -2, -8, ……, -290.

We have to find the number of terms in the given series, and the 30th term from the last.

Now, let us find the number of terms in the given A.P

We can find the number of terms by equating the last term to nth term of A.P, which gives us n value.

We know that, nth term is

$\mathrm{t}_{\mathrm{n}}=\mathrm{a}+(\mathrm{n}-1) \mathrm{d}$

where a is first term, d is common difference.

In our problem, a = 10, common difference (d) $=\mathrm{t}_{2}-\mathrm{t}_{1}=4-10=-6$

Now, $\mathrm{t}_{\mathrm{n}}=-290$

a + (n – 1)d = -290

10 + ( n – 1)(-6) = -290

-6n + 6 = -290 – 10

6 – 6n = -300

6n = 6 + 300

6n = 306 = 51

So, given series has 51 terms.

Now, let us find the 30th term from the last.

We know that, p th term from the last will be $t_{(n-p+1)}$

So, 30th term from last $=\mathrm{t}_{(51-30+1)}=\mathrm{t}_{(52-30)}=\mathrm{t}_{12}$

= 10 + (12 – 1)(-6)

= 10 + 11 x (-6) = 10 – 66 = -56

Hence, number of terms in the series is 51 and 30th term from last is -56.