Question

the first and last term of an AP and -3 and 145 respectively if the common difference is 4 find the 12 term, the 25th term and the the number of terms in the AP​

Answer 1

Answer:

Showing results for the first and last term of an AP and "-3" and 145 respectively if the common difference is 4 find the 12 term, the 25th term and the the number of terms in the AP

Answer 2

12th term of AP = 41  and 25th term = 93  

Number of terms in AP = 38

Given:

The first and last term of an AP and -3 and 145

And the common difference d = 4

To find:

Find the 12 terms, the 25th term and

The number of terms in the AP​  

Solution:

Formula used:

The nth term of an AP is given by

              T${n}$ = a + (n-1)d  

Where a = first term and d = common difference

Given that

First term a = - 3

And common difference d = 4

By the given formula,

n th term of given AP  = -3 + (n-1)4 = -3 + 4n - 4

=>      T${n}$ = - 7 + 4n

From above calculations

12th term of AP = - 7 + 4(12) = -7 + 48 = 41

25th term of AP = -7 + 4(25) = - 7 + 100 = 93

Here Number of terms in AP = Number of the last term

Let us assume that nth term is the last term of the AP

From the given data, nth term = 145

As we know, T${n}$ = - 7 + 4n  

=> - 7 + 4n = 145  

=>   4n = 152  

=>     n = 38  

Number of terms in AP = 38

Therefore,

12th term of AP = 41  and 25th term = 93  

Number of terms in AP = 38  

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